It's schrader (the car type valve)... I guess I pulled the pump head a little bit to the side, which tore it, but the air pressure trying to escape fast coupled with my removing the pump head at this point caused it to come completely off.

It was the weirdest thing (the wheel slipping). The ground wasn't wet, and our most recent precipitation (in the form of snow) was on Wednesday. I thought it was so cool the first time, so at the next street light that had turned red, I tried it again and was able to reproduce it (again without falling).