"My take is that any cooking method that does not have a control valve is prohibited, nixing alcohol and Esbit stoves as well. I'm sure that is all up to the Ranger du Jour and if you ask at an office, you will get the standard canned reply."
That is the common official restriction. Some backcountry rangers have been known to cut you some slack on an Esbit stove since it can't really become spilled liquid. But, there is no consistency. The story version that you get from a Forest Service office will vary day by day and with the phases of the moon.
You know, some of the national parks developed a good method of describing what was legal for bear canisters. That used photos of several brands of bear canisters, and when you went to get a wilderness permit, the ranger had you pick out the one that you were going to use. In a few cases, the ranger would make you haul it out of your pack to show. They could apply this same method with stove photos. You would have to pick out the stove photo that matched your equipment, and if you picked out a bad one, you wouldn't get a permit, or at least there would be an ugly notation "No cooking at all" on the permit.