The flight attendant became suspicious when the father spent an extended period of time in the bathroom before take off and then she discovered the toilet was broken. She alerted the authorities on that basis and the plane was called back from the runway and the family ejected.
Scott Brockman, Memphis International Airport’s Executive Vice President and Chief Operating Officer explained “My understanding is they were dressed in attire that would indicate some Muslim type religion.” I am not sure now many “Muslim type religion[s]” there are but Comair insists that this has nothing to do with the fact that they were wearing traditional Muslim clothing. It appears that if you linger too long in the bathroom (which might have something to do with the fact that the toilet was broken), you are likely to be thrown off a flight with Comair.
The family was allowed on a later flight (and presumably avoided the bathroom).
Comair is a subsidiary of Delta.