Lyft has a deal in place with Hertz, but they also have something called Express Drive. You pay Lyft $200/week, you get a car with maintenance and insurance included. There's a Lyft Express Drive/Rental depot in my town and I've seen mostly Hyundai Elantra/Sonata there.
Uber works with Enterprise but they have a similar plan with Fair - get a car on Fair as an Uber driver, pay $200/week. You get some flexibility on cars, I've been in Fords, Nissans and Hyundais from Fair as a passenger. Same deal - maintenance through Pep Boys/Aamco and insurance provided.
Lots of Uber/Lyft drivers don't have good credit - most of them bought new cars on subprime notes. The local Toyota dealers here were wheeling and dealing on Prii and used cars for Uber drivers.