On the chamber round+fireman thing: I've seen the video of packaged ammo in fires too.
A chambered round is a different situation. I suspect there are a lot of variables there - what's the rate of heat rise, does the powder degrade before igniting, soes your safe have 3/4 in thick walls, or 10 gauge, and so on. I've never heard of any injuries from it, so I suspect the odds are pretty low.
That said, if I was standing in the street watching firemen working on the roof over a safe where I'd left a rifle with a chambered round, I'd feel duty bound to inform the firemen. And I think the odds are fairly good that that knowledge might cause them to back off a bit. And since I'd want them fighting the fire aggressively, I keep the chamber empty (I chamber a thing called a 'Saf-T-Round', that ejects when you cycle the action, and has a orange arm sticking out the ejection port so you can't forget). Since I always store them that way, I think I'll remember to cycle it even in extremis.
As mentioned, putting something bulletproof in front of the muzzle would work as well.
YMMV. I just couldn't handle standing there and not warning them, no matter how slim I thought the odds were. How would I feel if the million to one event happened and one was hurt? I couldn't live with that.