I imagine doctors are rarely hired "cold" - they have some sort of prior relationship with the hiring institution or someone working there. E.g. they are already consulting there, or another doctor who works there has worked with them closely on a case etc.

Same for lawyers. You'd be targeting someone whom you've dealt or worked with in prior lawsuits (maybe they were the opposition counsel), deals (counsel for the other party), or complex cases involving multiple law firms working for the same side.