It is not about what the animal intented. It is about what humans intented (read again). Humans did not intent an organism to escape it’s enclosure and roam around. Thus, per iNat definition, it is in that instance (time and place) wild… an organism might change it’s iNat definition of wild/not wild over the course of it’s life.
I think you make it look harder then it is.
You might not agree to the wording or definition itself… but it still works best in iNat universe. At least I did not see a feasable alternative so far, that works better