If that is true, then what is to stop a company like Gilead from just paying them 2x or 3x what other small drug companies offer, so that hospitals will only do Gilead's trials. Thereby preventing other companies from getting their trials run.

Is that how Gilead gets so many results for so many so quickly?
They just throw money at the hospital to run the trial and the hospital can't refuse cause financially it is such a good deal?