How to fall safely while indoor bouldering

So... it happened again at my gym today. I witnessed a girl break her arm while climbing.. A good reminder of the inherent risks of bouldering. Even with those huge mats a bad landing can still lead to some serious consequences, especially for inexperienced climbers. see: How to fall safely while indoor bouldering

It got me thinking... is it possible that we've lost some of the caution that came with climbing outside, without mats?