I'm another who has helped push-start a car when out on my bike. Same experience of other motorists sitting in their cars pretending they haven't seen it, even though they are stuck behind the stuck car.
On the organised ride I was doing last week, day three started with a long, fast descent out of Bath Uni, with a T-junction at the bottom where you turned right. At the bottom was a rider looking at his bike and scratching his head. I did the usual 'You alright?' to which he replied with the usual 'Yes, thanks' but he clearly wasn't, so I stopped anyway. He reckoned his rear brake had jammed against and wasn't sure what to do. Well, that's an easy one - you just wrench the brake around its pivot bolt until it's aligned, right? Only this didn't help and the rear wheel still wasn't spinning freely. On closer inspection, it turned out the wheel was totally pringled and was jammed against the seatstay. The tyre was also incredibly hot, so he must have done the whole descent with it like that.
The odd thing was he had no recollection of hitting a bump or anything that could have caused it. And he reckoned his wheel had been fine when he finished the end of day two. I told him sorry, nothing much I can do about that. Luckily the event had mechanical support with spare wheels, so I left him to give them a call.
Over the course of the nine days, I helped several people, including one chap who was having trouble reinflating his tyre after a puncture because it turned out he'd put the wrong tube back in. I figured it would be good karma. Actually, I did get one puncture, but that was mainly because I'd let some air out of the tyres on a stretch of particularly poor road surface and then hit a stone, causing a pinch puncture (wouldn't have happened if I'd been running tubeless, as the tyres/wheels were intended to be), but I had changed the tyre and was on the move again before any other rider passed me so didn't have to go through the ritual exchange.
Also fell off on another occasion due to not paying attention and drifting too close to the kerb. Did an amazing judo roll onto the mercifully soft grass verge. There was a rider about 50m behind who enquired after my wellbeing as he passed but I was too busy laughing at my own stupidity to give him real cause for concern.