How is the AI restoring his own religion?

I'm quite certain you're wrong on that, as I recall doing just that in games and not being able to wipe out to Religion entirely.

The Holy City will always generate some influence to convert itself back to its founding religion.

You're right in that he was wrong but you are missing a little in your second statement.

Holy cities pressure themselves. No matter what, no matter how many times it changes hands, no matter who has been wiped off the face of the planet, holy cities always provide a good amount of pressure of their religion to themselves.

However, if a holy city ceases to be, it will, of course, not cause that pressure. If a holy city is razed, it's gone (they are generally capitals, but I have seen the AI found their religion in other cities, as well), of course. The other option is if it is hit by an inquisitor of another religion (from an enemy OR yourself), it'll purge the holy city title from it.

Note that while GPr's are generally thought to be missionaries and inquisitors, they are NOT. GPr's remove other religions but they do not act as inquisitors, seemingly only in the fact they do not remove a holy city from another religion (it is only hidden until there are followers in that city again).

A holy city that is purged by an inquisitor is no longer a holy city, and if converted back to the original religion, will not produce any pressure on itself again.
 
Note that while GPr's are generally thought to be missionaries and inquisitors, they are NOT. GPr's remove other religions but they do not act as inquisitors, seemingly only in the fact they do not remove a holy city from another religion (it is only hidden until there are followers in that city again).

A holy city that is purged by an inquisitor is no longer a holy city, and if converted back to the original religion, will not produce any pressure on itself again.
Oh really, that confirms what I had seemed to notice, but I didn't know that the city lost status of holy city completely even if liberated. That's nasty, but good to know. On a sidenote, I wonder if this function of Inquisitors was intended or a fault in the programming.
 
The other option is if it is hit by an inquisitor of another religion (from an enemy OR yourself), it'll purge the holy city title from it.

Good to know that, although you need to capture the city since inquisitors can not "work" in foreign cities.
 
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