I genuinely don't know how you interpret "I'm sure you understand the difference" as "you actually believe this". But sure, I'm manipulating your mind.
The evidence - well, an argument, because this isn't a paper - is exactly what you so helpfully brought up the Papal States for. Apart from literally his own domain, the pope did not turn any other nations into a Catholic theocracy because their monarch was Catholic.
It should be the other way around really - this idea of Catholic blind obedience to the pope is advanced as an assumption hy British historians despite having no example or evidence that it would be the case other than "that's what Catholics are like" despite the Anglican church literally arising from a Catholic English monarch disobeying the pope.
I didn't put any words in your mouth... I really don't understand how you're not getting that. I said you understand that it's not true. Literally just read the part you quoted.
Actually none of what you said just now was untrue. The leap that is unexplained is that bringing back a Catholic monarch would turn the UK into a papal theocracy where no other Catholic kingdom was (except the Papal States!).
And that specifically is the part that I'm arguing has no basis in fact - you're asking me to provide evidence that something wasn't going to happen. Usually we ask for evidence of speculation, not against speculation. It doesn't help that the people that could have said so were hung drawn and quartered, and the history written by people who immediately brought in further anti-Catholic legislation.