Treewells and minor avalanches do exist in bounds, so there is always the risk. I don't really think you need to take an avalanche class to ride inbounds, but some knowledge of what to do in bad situations is a must. Maybe more importantly respect ski patrol closures and warnings (most of the deaths lately have been people ducking ropes).
Shit happens, I dug a guy headfirst waistdeep in powder out last season who was suffocating, right in the middle of a designated run (one that wasn't used very often).
PowderHound and TreeNinja