Well, this depends on the state of mind BL was in. If we assume the earlier statements by SB, that he went for a hike, nothing out of the ordinary about it, his parents weren't immediately concerned then, sure, no real reason to call anybody.exactly my point. he wasn't missing, he wasn't a poi. so why are you saying they should have reported him missing?
If we use the recent statements, he was grieving, extremely upset, CL wished he could have stopped him, and consider that in light of everything else that was going on, missing person seems to move a little higher up on the list of possibilities at the point. The situation becomes a little more urgent.