I suspect it is a local regulation. A few years ago in the Gila Wilderness, during fire season, I seem to recall that only canister stoves were permitted. Of course, you are correct in thinking it arbitrary, but it is an easily recognized boundary, and there is some rationale behind it.

Consider what happens if your alcohol stove is upset. Either my Trangia or Super Cat would spill flaming liquid on the surrounding area. It might not be a disaster if I had meticulously cleared the surrounding area, but it could easily ignite a raging inferno. A stove with a valve is more easily controlled and extinguished.

Any stove can malfunction with bad consequences and I really think when you get down to picky details like this, the wisest course is to go somewhere where the fire danger is not so great...

It is not unknown when the fire danger gets a bit higher for the forests to be closed to all recreational entry, no matter how many valves your stove has.....