It falls to the individual instructor, in the end, to deliver appropriate training which to my mind should aim to develop a pilot's ability to save his or her arse when the time comes.
Rules these days, for better or worse, are written in such a way as to overtly specify every little detail that in the old days would have fallen under the blanket of good airmanship or simply ability to do something properly or not.
Using the quoted Part 61 MOS excerpt as a basis, you could teach stalling pretty much any way you liked as long as you could put your hand on your heart afterwards and say you covered the sequences appropriately and passed on your knowledge so as to help create a safe and aware pilot.
This doesn't imply or enforce any difference from what instructors would have done 20 or 30 years ago, and leaves scope for any of the 'good airmanship' tips any instructor would want to pass on. The sometimes awkward sounding wording of 'elements of competency' etc. are just part of the worldwide phenomenon of trying to quantise and specify all those things which were previously assumed (and which could mean different things to different people). I'm not a big fan of this over-detailed waffle, but it doesn't mean the sky's falling.
I'm not saying the new system is great, but I just get sick of people automatically bagging it for the sake of it, chiming in with 'CASA is f***ed, Part 61 is f***ed and the whole future of aviation is f***ed' any time it gets mentioned.
If you're an instructor teaching stalling, teach it the best way you know how, ensure you cover the bits they tell you to cover and add all your hard-earned hot tips. No change there, no matter what set of rules we use, I would hope, and maybe all the new age quantification of human factors will prompt us to examine whether we actually try to teach that to students or just assume they'll pick it up by osmosis.