Any tolerances are not to be used intentionally though. See for instance en route tracking. You are not permitted to use en-route tracking tolerances to make minor deviations around weather.
Your authority to be below the MSA relies on you being within tracking tolerance for the approach. If you are outside the tolerance for the approach then you have lost ALL authority to be below the MSA. At this point your altitude is illegal and you must do what you can to make it legal again i.e. climb.
For these people who are proposing doing this, under exactly what circumstances do they imagine it happening? How much fuel do they have? What type of aircraft are they flying? Why don't they just do another approach or fly to an alternate? Why would they even
consider turning an already screwed up approach (out of tolerance) into an even more screwed up approach (out of tolerance and intentionally remaining below the MSA)?
It wasn't suggested to fly down to the MDA, but simply to level off, thus discontinuing the approach, and climbing at the MAPt.
If they are "hoping to get visual" then they haven't discontinued the approach have they? You don't "hope to get visual" during the missed approach.
I think that if you really aren't advocating for this personally, rather than "just asking questions" on the internet you should do some real research yourself and ask someone, i.e., CASA, with the authority to give you an answer that you won't repeatedly close your ears to.
Or just ask your self this,
"I have flown out of tolerance on an approach and decided to maintain altitude rather than climb. Subsequently I hit an obstacle that I didn't know was there, oops! Miraculously I survive but some passengers die (oh noes I didn't think that would happen!) How would a court view my action of intentionally remaining below the safe altitude for the position my aircraft was in?"