Yep, I was a supply packing fool before I even knew what to do either. I did flat on my first voyage on Candy and since I had no clue to work around my lack of quick release so I angrily hoofed it two miles home rolling her on her back wheel. Wow she got heavy fast!
When I was mountain biking my boyfriend made his son practice changing flats for racing so I joined in. I was good with the MTB, almost fast, but road tires are my nemesis.
Similar story, when I did the Tour de Cure this guy a little bit ahead of me pulled over with a flat maybe two miles in. His buddy pulled over with him and neither had any gear. Mind you we were on the metric century route so I have to imagine they weren't green as frogs. So I stop to help them and start handing them a tube (I brought two prepared for worst case scenario), levers, frame pump. They both fiddled around for a while until it became 100% clear neither had a clue where to even start. Okay, you can't change it, but look at it for a minute and figure out how to remove it at least.
I was getting a little panicky because I already left towards the back of the pack and I didn't want to freak out, kill myself trying to rejoin the pack and burn out before I got to the big climb. Fortunately the SAG came along and helped them out. SAG gave him a tube and I was reunited with my long valve stem tube. Good thing because SAG wasn't carrying any. I didn't end up needing either, but felt better having both.
"True, but if you throw your panties into the middle of the peloton, someone's likely to get hurt."