A Fake Priest Duped Oxford and a World-Famous Historian

While I agree with what you are getting at, I have to say that depending on the religion/sect/whatever, the term for their clergy do typically have specific meaning. Typically a priest has devoted their entire life to that religion, from an early age. Its more than just getting their doctorate in theological studies (which a lot (most?) of them have).

I guess a lot of "real" priests who are supposed to have studied in London universities are well read. They can talk to you about philosophy in breadth or depth, and about great works of literature. Not to mention comparative religion.

If other well read people really want to suss out a fake, they can do that quickly.

But even during a 4-hour dinner party there'd be no reason to go in weapons hot: it'd be small talk and light conversation.

I’m not sure if you’re asking out of genuine curiosity, but — the entire Catholic tradition is built around the idea of the Church, an organization. Ergo faking the credentials of a member of this organization would indeed be a problem.

The idea that a preacher / priest / Christian teacher doesn’t need authority from the Catholic Church comes from the Protestant tradition (which has been much more influential in the Anglo-American world) and is why you get much more variety in the forms of American Christianity.

What’s the difference between a fake engineer and a real engineer? Do you really need a piece of paper approving you to do math?

There is formal training so the priests understand the doctorines. Priests don't just start doing it with no training, look up a thing called a seminary (Catholic).

There are also degrees in theology for church of England priests for example.

In a religion that has a priesthood tradition, like the Catholic church, a real priest is one that has been ordained (I'm not sure what the correct catholic terminology would be) by someone else that has authority to do so. You can't just declare yourself a catholic priest. You have to be made a catholic priest by someone higher up.

Having undergone selection, training, testing, certification, and placement as a priest within the respective religion.

This is about a serious question as asking 'why cars have engines'. You can refer to Wikipedia, or any other resource instead of couching excessive ignorance, borderline bigotry in the form of a supposedly innocent question.