I have posted our experience with stoves on our trip to Alaska two years ago. But, I will mention it again since it the seemingly ambiguity to the rules may be pertinent.
8 of us flew from 6 differerent directions to Fairbanks. There were a total of 4 stoves. Two went through, in their packed luggage, without issue. One person, leaving from Binghampton, NY, was queried if they had a stove. He replied yes, and when the counter person began to say he couldn't take it the pilot happened to walk by. She asked him what he thought, he said as long as there was no fuel, it's fine. This was, I believe, United.
Myself and my teammate left on United from Manchester, NH. We put our packs into duffle bags, and encased in the duffle bags we left a few other items that we needed, but weren't in the pack (i.e. poles, boots, etc.). I also pulled by stove out, put it in an orange padded package, labelled it "white gas stove", and stuffed it in my duffle. I figured if something did get sniffed out, it would be easy to get to instead of ripping through 6 nights of camping gear. They'd see the label, verify it was OK (according to TSA standards) and send it on it's way.
At the counter, both my partner and I were asked, as an afterthought, if we had a stove. He answered 'no' (he didn't have one), and I answered 'yes'. Clue #1: LIE. She didn't check his pack, just sent it on it's way. I pulled my out and showed her. She asked if it was brand new, I said 'no, but it's completely void of all fuel'. She said I can't take it. She never opened the package to verify. Clue #2: LIE AGAIN.
She wouldn't let it on the plane. I brought the stove back out to our car in the parking lot. We had no keys, since someone was going to pick it up with the spare set. So, I put this bright orange potentially explosive device next to our front tire, and sent ourselves across the country.
Now, the others who were queried about their stoves just answered 'no' and got through without an issue.
When we got to Fairbanks, I asked a couple of TSA folks about what happened, and he said it's up to the individual airlines to make their own rules, but we should've been OK according to them.