Mistakenly assuming the tach as correct (which indeed is what we are taught) and suspecting the ASI could in this case have lead to a stall on final.
I would certainly hope you were taught better than that!
Go fly a few circuits with an instructor with the ASI covered up. Or even better, go out and do some airwork (stalls particularly, but also steep turns) with the ASI covered up, then go and do some circuits.
Relying on the ASI as your sole indicator of an imminent stall is very dangerous, and is not making use of all other clues that precede a stall.
I made the right decision.
Continuing the flight with an instrument consistently indicating out of the limits? Not sure I agree with you on that statement. You didn't break anything, this time, but that doesn't mean the decision was right.