My one time helping to operate a shelter (hastily contrived by my local CERT, no Red Cross involvement) we had less to give to clients and more austere conditions than you describe. Most notably there were no cots, just folding tables for people to sleep on. And yet, once the emergency had passed there was a group that didn't want to leave.

When interviewed by shelter staff it turned out that none of them claimed to be homeless or far from home, and only a few needed a ride to go anywhere.