I went to the bike store yesterday to get new inner tubes, and maybe new tires.
Told the guy about what happened. He nodded, picked up a wheel and said "what most likely happened is that the tube got stuck under the bead and then ripped because of being pumped up." Duh. I did think to pump it up a little bit before putting the tire in, but I didn't pump it up before putting the tube in initially, which is probably why it happened.
He also said that it almost certainly didn't damage the tire, so I didn't spend 30+ each on new kevlar-belted tires, especially since he said that they will help with glass, but not things like the staple that got me this time.
Replaced the tube again today. Still need to do the brake pads, maybe tonight. Also need desperately to clean it!