I’m going to go against the grain here, and say Stephen would never go against his physician’s oath to help Jack. There have been times when Jack simply asked for information about the health of another officer, and Stephen either replied coldly or damned him to hell.
I see no reason to believe this - by the time Napoleon died, you couldn’t just sail up to St. Helena and say hello to him. There’s nothing in the books to suggest this.
There is an amusing fanfic story on hmssurprise.org though, where as a young Lieutenant, Jack stabs Napoleon in the leg at Toulon, and a young, still idealistic Stephen is the doctor who treats him.
“It would have been a strangely hasty, agitated meal otherwise.”
Having said that, he didn’t purge the midshipmen out of vengeance - he wanted the bones to see if the madder he had been feeding the rats had been absorbed into the skeleton. He was acting strictly in the interests of science. And Babbington got a pass on the boluses- he had just been promoted to acting third Lieutenant, and was no longer one of the young gentlemen.