Not necessarily... even an independent contractor can be expected to do a job for the client at a rate the client has specified or else not get the job for that client at all. You can argue that an independent contractor could still negotiate their price, but if the client doesn't want to negotiate, then that's still exactly the same story.
If Uber workers were independent contractors, then Uber, in this case, would be the driver's client, not the passengers, and Uber, as it happens, has specified the rate they are willing to pay. Dissatisfaction with how much one is making by no means any kind of pre-requisite for being an employee.
If, however, Uber workers were truly independent contractors, they could freely subcontract other drivers to drive multiple passengers at the same time and get paid for all of them (and presumably pay their own drivers a percentage of the rate that Uber offers per ride). Uber disallows this however, thereby exercising too much control over the work that their drivers do, and clearly placing them in the category of employee.
How much the workers make and how they cannot negotiate the price with the passengers is as far removed from what makes them employees as is imaginable, because actual independent contractors could easily be in the exact same situation. If an independent contractor can't find work at a rate that is satisfactory to them, then that is not the fault of those who might otherwise hire them, and does not make them employees when they happen to accept a job they are only taking because nobody else has jobs for them.