No, the traditional cab companies do not have to cover this market by law. I am aware of only one cab company in the DFW area (Yellow) that offers wheelchair vans as an option. A quick search shows that there are plenty of cab companies around the US that do not have wheelchair capabilities at all.
Also, for the record, small cab companies were allies of Uber here in Dallas.
"When a wheelchair accessible vehicle is requested, the operating authority must provide a wheelchair accessible vehicle, or cause one to be provided, without unreasonable delay."
Highlighted for emphasis. The cab company does not need to own or operate the vehicle. They just need to make sure the customer is provided with one at the same rate they would charge a customer who did not require one. This is not the same as what was originally stated above.
Also, for the record, small cab companies were allies of Uber here in Dallas.