There are probably as many opinions as possibilities unfortunately. What I would be most concerned about is that whatever it was, is bound to come back to feed at the trough. I would be locking them in at night, I do with mine, and I have a fenced run. It's hog wire with chicken wire attached to it. Regular chicken wire won't keep much of anything of large size out (i.e. dogs/coyotes).
The forensic chicken evidence aside, did you happen to see any tracks? If I had to put money on it, I would say it was 2-3 coyotes. Got a few bites, grabbed what they could carry and split. I don't think a dog would carry one off (of course possible). Kill and eat some sure, but I believe you would find all the bodies. Those dang things...don't get me started. Plus, what your neighbor alleged. Time to get the neighborhood watch eliminating the threat.
Off topic, but funny story:
I had a large cat stalking my chickens on Sunday. I went flying out back and I threw the closest thing I had, a stick, and missed completely of course, and it took off and ran into my chain link fence full speed, picked itself up and ran off. Hopefully he won't come back to the "crazy's" house. Mind you, this was no ordinary house cat, it was enormous. It was stalking my one and only banty hen (she just showed up one day).