A good topic... and discussed in our airline.
Firsly, it is "interesting" but irrelevant what the ATC rules are. The key here is the message has arrived, and in fact you do not have time to verify if it is ATC, another aircraft, or Johnny F*rtpants wiht a handheld in the car park.
Secondly most TO Briefs have a "cutoff" speed (not V1). Below stop for anything (within reason), above stop for serious stuff. I'd put an "RT Stop" in the first category only.
Thirdly you stated "
Airplane is unsafe or unable to fly." - this might cover it.
To me, above the cutoff, I would not stop based on an RT call alone. Hopefully the RT call, or it's context, would give some indication of "why" and that might draw one's attention to it and asses on that.
Finally:
However I fly with one Captain who also includes if ATC tells us to stop. Is he correct?
I would say no as a "compulsory stop".
If ATC ask you to stop it will be for a good reason
Disagree strongly!
NoD