Like I had a horse and he was pretty quiet and good on the trail BUT (this is my but) he once saw an emu and totally freaked out. I don't blame him, emus are kinda scary and no one was expecting it to be there. I didn't see another emu but if I did he'd probably freak out. I'd still consider him well trained for the trail, or good on the trail.
I had a well trained jumper BUT (another but) he was afraid of water, although this didn't cause problems because we only ever came across fake water jumps. This may diminish his ability to successfully compete at higher levels, but he was still well trained at jumping, and an invaluable horse to learn on.
So I think it is a matter of degrees. Like if a horse fulfills 98% of a criteria for whatever label I think that is enough, because all (or at least most) horses are going to have their weaknesses, and their attributes that stop them from being 100%.
Saying that though you do have a good point about a lot of people who do the my horse is great BUT... Like those people who say my horse is well trained BUT he bucks, I think that is way off. Or people who say my horse is friendly BUT he sometimes kicks.... etc. I guess people want to feel better about their horse, no one wants to say "my horse is terribly unpredictable because sometimes he seems well trained and other times he is bucking and I might die".
So I think I view it as a sliding scale, there can be slight "bumps" or imperfections that still pass, but the bigger stuff, well that's just people fooling themselves.