Let me clarify ....

TL;DR - it's hyperbole. answer the negative. if they didn't get this permission from you - you could sue them for copyright infringement. every service does it. don't freak.

Long Version:

The key to the text is "non-exclusive" - generally this grants the nonexclusive rights to display the material on a Web site. It also allows the licensee (ala DropBox) let their company use, manage, display [etc] your files.

It's a fairly standard contractual term now days - for example see

http://www.youtube.com/t/terms at 6 C OR even your Gmail Terms ... [http://www.google.com/accounts/TOS?hl=en at 11.]

Youtube - "For clarity, you retain all of your ownership rights in your Content. However, by submitting Content to YouTube, you hereby grant YouTube a worldwide, non-exclusive, royalty-free, sublicenseable and transferable license to use, reproduce, distribute, prepare derivative works of, display, publish, adapt, make available online or electronically transmit, and perform the Content in connection with the Service ...."

Gmail - "By submitting, posting or displaying the content you give Google a perpetual, irrevocable, worldwide, royalty-free, and non-exclusive license to reproduce, adapt, modify, translate, publish, publicly perform, publicly display and distribute any Content which you submit, post or display on or through, the Services. This license is for the sole purpose of enabling Google to display, distribute and promote the Services and may be revoked for certain Services as defined in the Additional Terms of those Services."

Generally, the language uses "non-exclusive" in its context which is OK. It basically allows internet services to be internet services

i.e. if they didn't have a non-exclusive licence, how could they use your files - which contain copyright content you own - in their services ? - they couldn't :) By asking for a non-exclusive licence, it means you are permitting DropBox to use it for the purposes of

"worldwide, non-exclusive, royalty-free, sublicenseable rights to use, copy, distribute, prepare derivative works (such as translations or format conversions) of, perform, or publicly display that stuff to the extent we think it necessary for the Service."

If you're uncomfortable with this term, then unfortunately you'll be uncomfortable using any service on the Internet as it's generally required to provide a service :) The terms agreement incorporates their Privacy Agreement - thus meaning they still owe you the obligations outlined in their privacy clause. They cannot distribute your content without your permission.

"But, but, but .... they should have to identify copyright not me"

Again, you are giving them to non-exclusive right. If you have MP3 music [legally obtained for example] - you have ownership for that file. You are provided with the right to store that file for personal use just as you have the right to share that file with your friends. The rights associated with this file are governed by the terms of service when you purchased that file [i.e. iTunes]. Go and read your rights regarding MP3 Music purchased from iTunes.

You are providing DropBox with a non-exclusive right - not an "exclusive right" which would be just that "exclusive" and therefore you have licensed it only to DropBox per see - to be able to storage, transform ... etc that file. The Privacy policy is incorporated within the Terms agreement - thereby inferring they cannot "distribute your content without your consent".

Dropbox do NOT "know" where you purchased the file or the terms surrounding every single file they store on your behalf [how could they?] - it's your responsibility - not theirs - hence the point of the term.

"You must ensure you have the rights you need to grant us that permission."

Dropbox is fine. Use it. Or stop using Gmail and most other services ....