I'm curious, did the cat have a tag or was it chipped identifying it ? Absent of any evidence to the contrary I can see how they might think its a stray. I get that it worried you but did they have a means to reach you to advise you they found it?
Cat's are almost impossible to collar when they don't want to be and she get's chipped soon. If a cat is outside and it's really friendly then it's not feral and the assumption should be that it belongs to someone. I was able to connect with them thru a facebook lost and found for the city.
Maybe I'm naïve but I have found random animals wandering, including a mother cat with new kittens that got into my yard. Neither the mother nor the kittens had any tags (we check for rfid chips too) so we got them rehomed. If there is a collar/tag and a means to reunite them with their original homes I'd jump at the chance.