The only time that's ever happened to me was as a teenager, when I (probably) overinflated the tire to begin with (with a gas station's compressor and no tire gauge) and then parked it in the sun all day, where the heat increased the pressure even more.

It seems to me that even if the tube was faulty, it wouldn't blow the tire off the rim unless it was overinflated?? The bead of the tire should still hold the pressure. Conversely, if the bead alone were faulty, I would think that you'd wind up with pinch flats while riding, not spontaneous ones.

Can you check your tire gauge against someone else's? (Check in a similar pressure range, not e.g. checking a high pressure bici tire gauge on a car tire.) That would be my first suspicion.