Q:

Should car sharing company explicitly notify about accident liability when advertising? 

On a car sharing company website, it advertises only benefits of its service but doesn't explicitly notify about insurance and liability in case of accident.  Should car sharing company explicitly notify about liability before booking? 

A:

How Are Liability And Insurance Matters Usually Disclosed? 
Normally, in a car sharing arrangement, you must establish a membership or account with the car sharing firm that includes all of the terms and conditions of the agreement between the parties (at least by reference to a document that you acknowledge that you have had an opportunity to read), often in connection with downloading an app necessary to use the service. 
I also strongly suspect (as a comment below indicates) that if you dug around enough on the firm's webpage that a link to the relevant terms and conditions could be found, even if it wasn't in the most obvious place.  But, this information will often not be on the firm's main landing page of their website, and can instead often only be reached with multiple clicks and/or drop down menus. 
Sometimes this is called a "terms of service", sometimes this is called a "master agreement", sometimes it is called a "membership agreement" or "account agreement".  My list of names for this agreement is not exhaustive.  Often these terms are also described elsewhere in simplified form, such as a "how to" brochure, or information that is posted on the interior of the vehicle itself or in a sleeve of documents in the car. 
Usually, in the course of the sign up process there would typically be a box to click and a link or scrollable portion of the screen at which you can review all of those terms and conditions which are the terms of the contract. 
What Must Advertising Say And Why? 
It is not generally necessary for the advertising itself to disclose every term and condition and detail of the arrangement.  Generally speaking, an advertisement is considered merely an "invitation to make an offer" to enter into a contract, rather than an offer which can be accepted directly and form a contract.  Of course, a particular jurisdiction's legislature certainly has the power to require that a car sharing company disclose liability and insurance information in a particular fashion set forth in a statute or regulation, if that jurisdiction's legislative body chooses to do so. 
Even when these issues are mentioned in advertising (even when some disclosure is required by law in adverising), usually this would be in the form of a sentence that incorporates another document by reference like "Additional terms and conditions, including terms and conditions related to liability and insurance, that can be found at . . . .  apply." 
This is due to the practical reality that TV and radio ads are usually just 15-60 seconds allowing about 25-100 words or perhaps a few more if the announcer speaks quickly, and that ads in print or on a screen also typically have room for only a very small amount of text. 
Websites, in principle, provide an effectively infinite amount of capacity to host content, but considerations of ease of website use and the need to make the landing page striking for marketing purposes (as well as the need to make websites mobile user friendly when that is the only way that many Internet users can access the web) usually relegates the legal terms of the agreement to less attention grabbing locations. 
Often, these terms are disclosed more conspicuously when the terms and conditions change materially, something that often has its own little PR campaign accompanying it. 
Unilaterally Imposed Contracts of Adhesion
One reason that disclosure isn't such a huge issue is that car share agreements are almost always mass produced, not up for negotiation, "contracts of adhesion" that only senior management of the firm has the authority to modify.  In the case of these intangible contractually agreed services, the terms of the agreement are more akin to a non-negotiable product design than to the paradigmatic haggled legal agreement between parties. 
Thus, a customer has only two choices.  Use the service according to the standard terms, or don't use the service. 
Given this reality, the average buyer of the services relies upon the market place rejecting contracts of adhesion with bad terms, upon testimonials (good and bad) from prior users of the service, and upon media publicity for notorious terms or incidents that makes it look like the business doesn't treat it customers well, to keep the agreements reasonable, rather than upon individualized decisions to use or not use the service based upon a detailed review of the contract terms. 
There are legal doctrines pertaining to contracts of adhesion that invalidate terms that are unconscionable or not within the reasonable expectation of a consumer unless those terms of conspicuously disclosed. 
A classic example, for example, would be that a car share agreement that imposed extraction of a kidney as a fine for being one days late in paying an invoice would be void as a matter of law, even if the referenced document said so in bold large face type and the customer clicked a box acknowledging having read the agreement. 
What Happens If There Is No Agreement Or Disclosure? 
If there was never a step at which the terms and conditions were disclosed or accepted, then the default rules of law pertaining to personal property leasing, together with the laws pertaining to automobile accidents and insurance (both statutory and case law) in the jurisdiction in question. 
In almost all cases, liability to third parties for accidents is generally a matter of tort law or statute imposed by the government, rather than being something that can be modified by agreement.  Also, usually the government imposes minimum insurance requirements and the owner of the car also has an incentive (and often a legal requirement) to have car insurance in force. 
In the United States, the default rules of law pertaining to personal property leasing, are set forth in Article 2A of the Uniform Commercial Code, which has been adopted in every U.S. State, the District of Columbia, Puerto Rico, and each self-governing U.S. territory with its own internal laws. 
In countries Europe or Latin American or Asia known as "civil law" countries (i.e. in those countries outside the British common law tradition, the Islamic law legal tradition, tribal or clan or caste law, or legal systems with communist regime roots established in the 20th century), the equivalent default rules of law (governing personal property leases, contracts to provide services, leases and insurance) would be contained in either a civil code or a commercial code of that country in most cases. 
In common law countries, the contractual agreements tend to be longer than the default provisions of law are skinnier.  In civil law countries, the reverse is true. 
A hybrid of these two approaches which also limits the need of customers to monitor contract terms is the regulatory model commonly used in the insurance industry in the United States takes the reality that contracts of adhesion are the norm and gives it a regulatory twist.  In this hybrid model, all of the boilerplate language of every insurance contract down to the last word of non-customized or only semi-customized language, and often fee schedules as well, must be substantively improved by a state agency that regulates insurance.  In these models, a public official negotiates the terms of the contracts with the firms, subject to intervention in and participation in the process by industry associations and non-profits or interested individuals on behalf of consumers or other interested parties.  In these hybrid systems, the approved contract language which can't be modified in the boilerplate language by either the firms or the customers, is on file with the regulatory agency and provides constructive notice to all parties in much the same way as a statute or government regulation. 
If not enough material terms of the agreement (e.g. the rental rate) were disclosed to form a contract, then there would be no enforcement contractual arrangement involved in the car share and the car share company would have to rely on the law of unjust enrichment to recover the fair market value of the services provided in each case, which as a practical matter, wouldn't be viable as a business model. 
Distinctions Between The Two Kinds Of Car Sharing Arrangements
There is some ambiguity in the question because there are a couple main types of car sharing arrangements. 
One is more like a rental car and you drive the vehicle yourself (Car2Go is one of them).  In this case, the firm typically provides car insurance and does a limited background of a prospective account holders driving record before allowing someone to use the service.  But, the user of the service, who drives the car, would be primarily liable for any accident that the car gets into. 
The other kind, sometimes called a "car share" and sometimes called a "ride share" is more like an Uber or Lyft, which is a glorified, on demand taxi service, in which a driver provides the services of the driver and the vehicle and takes car of insurance and will be primarily liable for any accident the car gets into as a driver and owner of the car.