Aside from the question of fact as to where McCain was born, there is a difference between ‘The United States’ and “United States Territory’.
That’s why there was always a question about Barry Goldwater, born in the Arizona Territory before Arizona became part of ‘The United States’.
Of course, Barry Goldwater was a US citizen by birth - but like Ted Cruz or John Cain, only by action of statute law. For me that is a distinction without a difference.
IIRC, weren’t common law jus soli questions usually centered more on the sovereignty of the king (or government) ruling the territory rather than some specific status like “state” vs. “territory”?