I couldn't have put it better myself. I'd feel bad too, and try to do something nice, but at the end of the day...a dog is a dog. If a cat is lose it could be a stray or a pet and your dog has no way of knowing the difference-both are fun to chase.
I'd be infuriated that they took my dog away, though (she's easily scared of some men and other dogs). I'm not sure what they need to investigate here.