I suspect that when faced with reality and in a genuine life and death situation, most people would leave their pets. My experience in the Balkans, where people were literally turning on former friends, and they often had a matter of minutes to escape or be shot, people leave, if they even get the chance. A lot didn't get the chance to leave, killed in their own homes, and those doing the killing aren't wasting time humanely killing pets.
While not the same as in the ME, leaving on foot only with what you can carry, few are going to be taking a cat carrier or a dog on a leash. Its an extra mouth to feed. Turned onto the street, at least they have some chance of survival through scavenging.
If the only exit is on a plane not set up for carrying lots of pets safely and buying an appropriate hold crate isn't necessarily quick or easy, when faced with a choice of get on the plane now with your kids and no dog or stay stuck for an unspecified period and risk your kids, most will choose to leave. They don't necessarily want to do it, but what else should they do?