I was also surprised the first time I heard you can safely burn explosives: I was reading some comments on the Vietnam war from veterans talking about how they used to heat their meals by burning pieces of C4.
I mean, the fumes are super not good since there will be a significant amount of N20, but most explosives are very hard to set off. Sure, it's relatively easy to create chemicals that explode, but the real trick is finding ones that don't explode from the slightest bump. For example, Alfred Nobel didn't invent nitroglycerin, he invented a safe(er) way to store and transport it. TNT is actually relatively difficult to set off, even something like shooting it with a rifle won't necessarily set it off. That being said, explosives definitely can sensitize with age, which is why unexploded ordinance is so hazardous.
For reference, my father was an explosives engineer and was the point of contact for local law enforcement when they found old explosives. (this was the 90s,so they didn't have funding for a bomb disposal team and this was an area that had mining history). There were multiple buildings where he advised the safest way to deal with the old explosives (mostly dynamite, but some TNT) was to set an explosive charge near and set them off since handling them would have been too high risk. New dynamite is safe enough you could toss it onto a campfire and it won't do anything more dramatic than burn rapidly (EDIT: not a guarantee, it is potentially possible that a fire could set dynamite off so I wouldn't recommend this, but anyone who can purchase it has an explosives license and hopefully knows better), but once it has aged enough it could potentially be set off by poking it with a stick. More modern explosives like TNT don't break down quite as dramatically, and in certain conditions TNT can even be rendered inert, but given unknown environmental factors any improperly stored explosives should be treated as potentially ready to go off if they are poked gently. That said, dad definitely did dispose of the majority of the old explosives simply by burning them, sometimes in place with the fire department on site if they couldn't be safely moved. The only buildings he had to set off the old explosives in were outbuildings in remote areas, where they had been left alone for a very long time. One of the structures, he was able to see a date stamp of 1918 on the wooden crate of dynamite leaking raw nitroglycerin.
