Great idea XRX! Great opportunity to learn from other people's mistakes.
Vid 1: We can't see what happened just before the video starts, but the rider may have been coming in WAY too hot for the turn, and was trying to slow down as much as possible before leaning (because we all know it's bad to brake while leaning, right??). But his mistake was he never stopped braking and started leaning. I think he had already reached safe cornering speed by the time his tire started sliding, but he wasn't mentally ready to start the lean. In his mind, stopping before hitting the rail was his only focus. You've got to know these bikes do NOT stop quickly, but they can maneuver like nobody's business. Trust your tires. If you're going to hit the rail anyways, better to lean and lowside than hit the rail upright and highside over the side of the mountain.
Vid 2: It's a little harder to see the mistake in this one. It just looks like he leaned farther than his bike could handle and the tires let loose. Maybe the tires were bald on the edges, or maybe they weren't really broken in, or maybe the extreme edges of the tire hadn't warmed up sufficiently yet. The lesson here is don't take the first turn at full lean; gradually increase the lean on each turn so you give the edges of your tires adequate friction to heat up before you go full lean.
It's also possible his tires didn't let loose until something else got caught between the bike and the ground, like his foot, lightening the load on the tires and breaking traction. In this case, he was simply going too fast. You can only lean so far. I also noticed his body's not leaning off the bike at all. In fact, he appears to be counter-leaning. I've heard it's better to shift your weight off of the bike and into the turn, so you can keep the bike a little more upright and improve cornering. XRX, as a racer and track instructor, is this tip accurate, or was I misled?
Finally, the lesson I learned from the third video was always have insurance if you can't afford to buy a new bike. Not all wrecks can be repaired with parts on eBay.