The key point here is that all teams will eventually tune out there coach, it just comes down to how many seasons it takes to happen. Those teams in which we see having elongated success patterns with the same coach at the helm (like Scotty Bowman) tend to have both exceptional coaches and exceptional on ice leaders.
In the Kings' case, they neither had an exceptional head coach (I can't really evaluate the assistant coaches) or exceptional on ice leadership - but likely they did have a very good HC and good on ice leadership to make as much progress as they did and keep it moving forward for 4 seasons. That said, it eventually fell apart and Kopitar and Doughty do deserve some of the blame.
On a side note, I would be very surprised if McLellan ever won a Cup as HC unless he learns to be much more adaptable. Seems like he gets out to an early series lead, the opposing team makes adjustments and shift the momentum only for him to stay the course and end up losing the series.