We divorced ourselves from Disney after they searched our daypacks (before terror concerns) and triumphantly pulled out a couple of apples and sandwiches. We were told to leave these in a locker and if we wanted to eat them, we had to do it right by the locker - there was one grim table there for the whole LA park! As we were reentering the park, the original gate attendant rushed in, to make sure that our packs were searched again.
Sure they wanted to be certain that the only food we were having inside was that purchased from them, but the paradox was that the only food they were offering inside were sugar bars and really bad fast food - no fruit, no nothing I'd want to put in my mouth. The divorce was sealed when we were visiting a safari a day later and our kid asked whether the animals we were watching were real - he was suspecting moving Disney mannequins.
My wife has a very particular diet and after telling the security folks that they let her bring her food in without any fuss. She told them right away so no searching was required and it probably didn't hurt that it was clearly only enough food for her and the rest of us would obviously be buying food from them. You may have run across one of the more zealous attendants.
A local theme park doesn't allow food past the gates either but they do have a large and attractive picnic area complete with grills.
The fake animal bit is funny. I found the safari to be one of the lamest attractions we visited at Disney but my then 6 year old liked it. When I was a kid, Disney parks seemed so far ahead of everyone else in terms of what you could find there. Now, not so much.