In California, Uber is covered by James River for their insurance, while Lyft utilizes York/Steadfast for their insurance. These insurance companies are large enough so that any single claim does not impact their bottom line in any meaningful way. So long as your claim is valid, and documented properly by the authorities such as police, ambulance, fire rescue, and your medical doctors, your claim will be given the respect that it should be.
Of course, in order to get the full respect of the insurance companies, it makes a big difference when you hire a law firm that has experience handling injury claims against a ridesharing company. Your privileges on the Uber or Lyft applications or platforms will not be in jeopardy because you have brought a valid injury claim.