I think it looks like that when you see if from the TB point of view. When you see it from the Capitals point of view. Having watched every game of every series, you see something different. You see a distinct pattern. Each series started off as a battle and ended with the Capitals coming from behind to control the final games of each series.
Its undeniable that they physically wore down their opponents. Like a football team with a heavy running game. The strategy doesn't play out til the end.
If you want to think that the Capitals just wanted it more, realize that getting beat up will deter your desire. Getting beat up with take the jump from your movement and make it look like you aren't hustling.
Maybe the Caps coaching was better. Maybe they wanted it more, but I would suggest that their physical destruction was a primary in them wanting it more and sticking with that game when behind in every series was a major factor in the coaching value.
But that's just my view