Generally speaking, from what I have seen "Defense of Life and Property" bear shootings are investigated. However, the authorities virtually always give people the benefit of the doubt. Unless you did something really egregious in front of witnessess you are very unlikely to get into trouble over a DLP bear shooting incident, so long as you report it, and make a good faith effort to surrender hide, claws, and skull etc. I know of at least one incident where the shooter was unable to recover the hide due to some extunuating circustances. ADFG wasn't pleased, but after some discussion they accepted his story and didn't hassle the guy further.

Obviously the reason for the DLP regs is that otherwise anyone who wanted a bear trophy but didn't want to bother with silly things like seasons, tags, etc could just go shoot any bear they see (threatening or not), then concoct some BS story about self defense, and get a nice bear rug to hang in their den. It is just a means of making sure people don't kill bears for no reason and then claim defense.