Just to clarify, the squirrel did have a container. (Not @ you specifically, @dommerdoodle.)
One may also note that no matter what an airlines’ policy, the TSA stance is that many animals do not pose a threat to the aviation system.
“The squirrel was screened the same way someone’s cat would be screened. The container was sent through the x-ray machine while the passenger carried the squirrel through the walk-through metal detector. In this way we could be sure that there were no explosives or other prohibited items hidden inside the container. Once the TSA determines that an animal and its carrying case do not pose a threat to the aviation system, then it is up to the airline to determine if the animal may fly or not.”
My view is that this is largely an issue of perception.
ETA: Just want to add, all animals should be kept in escape-proof carriers on a flight. It’s just basic courtesy. Like not removing your shoes, or not harassing fellow travelers.