That smacks of what I was told by the Triumph tech at castle Powersports when I asked them if they had a rubber washer and could I use a metric hex key. As soon as they found out what I wanted to do the answer was no, 'for liability reasons' even though they would not touch Raymond's bike at all, just me and with Raymond's permission. Of course they wanted to sell Raymond a Throttle Meister on the spot. No liability either real or perceived there. Problem was, they weren't getting the profit with my fix. Neither was I. I just wanted Raymond not to suffer wrist cramps or numb fingers on the way home. You fully well know about liability issues and trade dress because you and I discussed it, however, it seem to me as though the liability thing becomes a catch all when a shop don't want to do something that they are making a minimal profit on.
It's too bad you don't live around here. I have a good friend that owns a motorcycle repair shop that services all makes and he has a Snap-On tire machine that don't touch the rim either. Even though he sells tires he told me that whatever tire I bought, whether from him or elsewhere, he'd mount and spin balance it.
I'd run, not walk away from that tire shop and then bad mouth them to everyone. That's just good business practice on our parts.
You could mount it yourself. You'll have a ***** of a time dismounting the old one. I'd do what Gunshots did and cut it off. A die grinder and cut-off wheels should make pretty short work of the tire just be careful when cutting the bead cords and wear a particulate face mask. Mounting a new one will painful too but you could do it, I'm sure. If I can mount tractor tires myself, you can do a bike tire. Use plenty of lube (I use liquid dish soap in water) and good tire spoons (believe it or not, TSC sells top of the line tire spoons and bars) but they aren't cheap. You'll still have to get it computer balanced but before you do, make sure you pull the adhesive weights.
You don't need a BMFH to break the bead. You need no hammer at all. Only truck tires need a tire sledge or a tractor tire that has a really stiff sidewall. get yourself some good "C" clamps that have enough throat and depth to engage the tire at the bead, pull the valve core and crank those puppies down on the tire. They will pop the bead right off the rim and then use the spoons to lever it off the rim to one side. Stand the tire and rim vertically and then lever the other side off the rim on the same side as the first bead came off from. That is, if you don't cut it off. Another good trick is to lay the rim and tire down on a sheet of plywood and carefully engage the tire as close to the rim as possible with your front tire on your car or pickup truck. That will break it from the rim too. Just be sure to pull the valve core. Once you get the tire off the rim, be sure to turn the valve stem around the other way so it's easier to fill. I used to sledge tires on trucks and tractors but I went out and bought a Bead Cheeta which is basically like a can opener that's driven with a 1/2" impact wrench. The sledge is an ornament in the garage now.
Good luck. Actually it won't take any luck, just some good tools and a little time.
If you were here, I'd do it for ya. Plus, I'd install a FlipMeister, all for no charge. After all, that's what friends are for.