You've genned up on the situation, it seems. Good. You might even know a bit more than I can tell you, at the moment, if the Wiki is up-to-date.
Originally, the special requirement for a [PET_EXOTIC] (as opposed to something that was tameable but just as a [PET]) was that you have a dwarf known as the Dungeon Master. He disappeared from the game for a while (although you could add him back in, with modding, I hear) across a whole range of versions, for reasons I never took much notice of but was probably because the developer didn't think he could make the character work like he really wanted him.
As I said, though I don't really know how the situation is at the moment. If the wiki is as up-to-date as it could be, it might just be waiting for someone to narrow down the exact situation. If it's a little behind the time it might be thinking about the above Dungeon Master (and/or modding to allow/not need him to do this job).
The fact that it's (taking your word for it, not looked myself) contrasting the comparative magnitudes of difficulty, it sounds like it might be the former, as training always used to be of the "gets done if it can be done" kind, no real 'difficulty level', that I know of. But the dev-notes and player conversations that I've seen suggest that it's a now a proper skill-test.