The stall warning could be false in many such situations. If the IAS is too low, either from a high AOA or maybe clogged pitot tubes, for example.
The warning is inhibited in certain scenarios, and during the beginning of stall recovery, the inhibit could be removed as conditions improve, and the stall warning will sound again, even though you have done the right thing and are actually recovering from the stall. You actually need to continue stall recovery through the false warning.
What can happen with inexperience is that you do the right thing to recover, and the stall warning comes on.
You don't realize that the warning has returned because it's no longer inhibited by a low IAS, and that it will go away again as your AOA and airspeed improve.
So you either stop the stall recovery, or you actually do the opposite. This causes the stall warning to be inhibited again, so it quits. That reinforces the idea that you are doing the right thing, when you aren't.