An explosion is just a very fast (often in a confined space) burn. Types of explosives are categorized by the speed of their burn. If you put an incendiary (your word) into an enclosed space, you get an explosion. In any case, I'd say the number of hikers making and using thermite to light their camp fires and stoves compared to the number using Bic lighters is, uh, how you say, insignificant, if not nonexistant.
Also, Mister Knee, the term of art is "fougasse." The type of reaction, as you described it, is of a fuel-air explosion -- it's also a Vietnam War-era term for a type of explosive anti-personnel expedient using diesel and an explosive device to spread and ignite that fuel -- descriptions can be found in mil. field manuals of that time period. Another definition of the word is for a type of French bread, but you likely know that already.
Also, someone would have to check on this, but I'm pretty sure mixing up thermite reactions on federal land is ILLEGAL, especially in the context of hiking and camping. Telling someone it's OK to do this is not a good idea, not merely from a law enforcement perspective, but also from the fact that a person could get badly injured/burned or even killed doing it.
Calling someone clueless for suggesting that a Bic lighter is good for use on the Appalachian Trail transcends stupid and enters the realm of mental defect.
Just 'cause you seen it on the teevee doesn't mean it's good to do yourself. Unless you want to go for a Darwin Award. In that case, never mind the boring little Bic.