These are independent contractors. The doctors doing the work are the principals, and they get all the payout from the contract.

Government procurement doesn't work that way. Disability determination is a program funded by the US Social Security Administration, and comes with lots of compliance requirements that would be too expensive to implement for hundreds of contractors. Even if Tennessee allows you to give cash to random individuals, the Feds do not.

There is almost certainly a prime contractor who owns the relationship, who then hires independent contractors as subs. They probably collect a percentage or fixed fee for each piecework task completed.