Medicaid is the United States' program for providing health care to poor people. Medicare (for people 65 years and older) is administered by the federal government, while Medicaid is separately administered by each state.
"In some states Medicaid is subcontracted to private health insurance companies, while other states pay providers (i.e., doctors, clinics and hospitals) directly." - https://en.wikipedia.org/wiki/Medicaid#State_implementations
Arizona is a subcontracting state. The state government pays insurance companies to manage the services provided under the Medicaid program; the insurance companies pay the transportation companies to get people to their appointments.
> The comment even indicates that the taxi companies structures themselves around the insurance company contracts
It started out as a taxi company... Then "transportation vouchers" came along, so businesses could get people where they needed to go without having to give people cash for taxi fares.
Over the decades vouchers became a larger and larger part of the taxi company's business. Paper vouchers for drivers became electronic vouchers; pickups and dropoffs are scheduled electronically.
When the Apps came along the taxi company's business of leasing taxis mostly evaporated, so the company got rid of its taxi fleet and now focuses on its transportation contracts ("vouchers").
> I'm confused how the state is supposed to be in this too.
In the comment above I mixed up who pays for what, but ultimately the transportation funds come from the state government and federal government, filtered through the state's subcontracted insurance company.