Apparently James Hewitt and the late Lady Di met after (three years after in 1987) Harry was born, yet Harry
apparently believed the claims until he discovered they were impossible (
original link).
I read some random thing that the new Canadian PM Mark Carney (former Governor of the Bank of England) wanted Harry as Governor General, which sounds insane and likely just a joke. Even if Canadians are elbows up riled about Trump, Meghan and Harry would probably likely take too far. It was talked about independently of Mark Carney
a few years ago. It would seem highly inappropriate. Harry probably could manage, but not with Meghan around. Governor General posts were a traditional make work for certain royals where the devil makes work for idle hands, like Edward and Wallis. He was made governor of the Bahamas and did fairly okay.