Unfortunately, both of these scenarios happened as you each explained them. Brandon Lee was killed when a bullet that was lodged within the barrell ended up being fired out after a dummy round was shot in the weapon.
Jon-Erik Hexum was playing around doing a pretend game of Russian Roulette in between filming after the scenes weren't filmed up to the director's standard. The plastic/paper debris from the dummy round was ejected from the weapon and damaged Hexum's brain.
I recently began buying replica western weapons to learn how to twirl (like Tombstone or Revolver Ocelot), and it is beyond me how Hollywood film crews could not have a licensed firearm expert there to inspect and clear every weapon before every scene. After these earlier two situations with Lee and Hexum I'm not sure why they even use fully functional firearms anyway, given the accuracy of non-firing replicas which can use caps and the capabilities of modern digital editing. It couldn't cost them more than a few hundred bucks to get a very high-quality non-firing replica.