enargins

I'm not doubting that this is what may have happened. I'm only questioning why, if the tire slid off the rim, allowing the tire to balloon out and pop, that I didn't see it do it, since I was watching the tire the entire time. (The tire was off the bike in the back of my minivan while being inflated, and I was sitting next to it, holding it.)
Granted, I was only looking at one side of the tire. But that was the side of the tire which came off the rim. So if the tire came off the rim first, allowing the tube to balloon out, it seems I would have seen it, since I was looking at the tire the whole time, no?
Also (and, again, not arguing, just trying to understand): if the tube ballooned out and then popped, then wouldn't that have been where the tear was, where the ballooning happened? But the tear was along the seam, at the very outside of the tube, not on the side of the tube.
Thanks!