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Is this season one of House? There isn't really a trope for this exact situation (Too Rare To Trope), but according to Volger's character sheet it seems to encapsulate Screw the Rules, I Have Money! and a subversion of Wealthy Philanthropist.
The damned queen and the relentless knight.I'm troping one episode of House, where a few tropes caught my attention (the main patient's dead baby, 2 decades ago, being Death of a Child and Outliving One's Offspring, and the child born in this episode being a Posthumous Sibling); a background case of Abuse Mistake; and at the beginning the police suspecting that there's a Drunk Driver.

A person donates millions of dollars to a hospital. Then, when one particular doctor is forced to give a speech regarding the donor's product (It Makes Sense in Context), the doctor makes a negative one. The donor then tells the hospital board that if they refuse to fire the doctor, he will go away with his money.