I don't think a single escaped individual can be counted as wild, particularly if they haven't even left the grounds of the zoo! If they're from a naturalised population that is at least attempting to breed (whether escaped or reintroduced) then that would be different.
I generally use the rule that only established exotic or otherwise introduced populations count*. The problem with that system is the term "established", because that not aways clear. I count Dutch Nile geese, Rose-ringed parakeets and Pheasants because they have been living in the wild for generations. The "official" Dutch list doesn't count any introduced species except Canada geese and Ruddy shelduck for some reason (although the populations of the latter appearently may have some genuinely wild ancestors).
How about this case:
The National Park Hoge Veluwe (one of the larger Dutch reserves) has population of (re)introduced deer, mouflon and wild boar, and is fully enclosed but covers 5400 hectares. The deer can jump over the fences but the mouflons and boars can't. For the boars there are special gates, but they are now closed to inhibit the spreading of diseases, although a large number of boars probably won't notice it at all. The animals have to survive on their own, but are sometimes lured to certain areas for counting with some food. The numbers are controlled. Are these animals wild? According to the definition of @Kakapo, the neighbour's poodle in the example @Chlidonias gave is more wild than the boars and mouflons in this example, which to me is complete madness!
* Although I would not count animals like konik horses or cattle introduced to graze in a nature reserve, even if they have been living there for generations. It just doesn't feel right.