Sadly, I think that is correct.
I remember years ago Senator Rudy Boschwitz (who was born somewhere outside of the US) was always saying that he was the only Senator who didn’t think he could be President.
He said he knew he couldn’t be President, b/c he was born outside of the US. His point was that he was a better Senator, b/c he wasnt looking at the next rung on the ladder.
In any event...just an anecdote that is sort of relevant here.