While that's correct (only providers of fixed-route services like shuttle runs must be wheelchair accessible), there are a number of ADA requirements for private transport services[1]:

  Additionally, private entities providing
  taxi service cannot discriminate against
  individuals with disabilities by refusing 
  to provide service to individuals with 
  disabilities who can use taxi vehicles 
  and/or use service animals, refusing to
  assist with the stowing of mobility
  devices, or charging higher fares or
  fees for carrying individuals with 
  disabilities and their equipment than are 
  charged to other persons.

So you can't refuse someone with a service animal, even if you don't want service animals in your vehicle. And you can't refuse someone with a mobility device that can be stowed in your vehicle (such as a collapsible wheelchair), just because you don't want the hassle of the added time or inconvenience of helping stow away their device.

[1] https://adata.org/factsheet/ADA-accessible-transportation

So that means Uber is in full compliance?