Either the driver rented the car to a middleman who rented the medallion from a rich owner, or said owner was selling and financing (most banks won't touch these medallions!) a medallion at a ridiculous interest rate to a driver that plans to use it as his retirement savings.
Pre-Uber, the more I spoke to cab drivers the more it seemed their industry was a pyramid schemed aimed at helping established rent-seeker take advantage of often poor new immigrants. Uber brought a breeze of fresh air: Someone could simply buy a car, calculate the depreciation and it's value on the market (since unlike medallions cars are relatively liquid assets!) do rideshare and calculate their profits or loss. They can get out of the game at anytime.