Given all the dreadful things that are done to rabbits why make this such an issue??
Rabbits get far more stressed by someone faffing about worrying about how to handle them than by someone competantly turning them over to administer meds or groom them. Our rabbits are routinely turned over and we have more elderly rabbits living long happy lives than anywhere else. Mint for example is a lionhead with long extremely fine fur who has been turned over and shaved underneath every month for the last nine years. Many of our older rabbits have a daily dose of metacam dripped into their mouths while they are upsidedown every morning. They lick it up happily. It takes a few seconds and they feel more comfortable for the rest of the day. I always do it when I let them out so they know that I won't pick them up at any other time, so they trust me.
If a rabbit has compromised breathing of course you should not turn them over, but otherwise the faster interventions can be done the better. I don't say tranced because while some do get quiet in that position others don't, and I never make any attempt to induce it. I just get what is needed done gently but firmly. They don't enjoy being handled so why prolong it?
Discouraging people from holding rabbits up side down for cuddling is a good idea, they hate it. Discouraging this quick method of providing care for the rabbit is not.
IMO this is a well intentioned campaign that has gone too far.