There's a lot of truth to this statement...according to TSN, the Leafs have killed 31 of 32 penalties thus far. I'm more comfortable watching their PK than their 5v5 lately.
PK is not easy, but it's just system adherence and pure effort and willingness. So for a lot of hockey players, it's easy in the mental sense and just hard physically.
The Leafs offense, once they get into the zone, is quite good: lots of skill and creativity and they look consistently dangerous if given any amount of spacetime.
The Leafs set defense is also pretty good, forcing play to low danger areas, giving the goalies line of sight, and they have speed to the boards to make things difficult for the opponents.
Where they have consistently run into difficulties this season is in transition both directions: sort outs and breakouts. On the backcheck, D give up the line so easily there's too much speed coming into their DZ. On the breakouts, the D are playing above their stations and having trouble with routine outs (bad at easy passes) and adjusting when their original plan is being sat on (bad at reading). So lots of turnovers are happening in bad places, which kills momentum at minimum and more often than not ends up in the net. If Stolarz isn't playing like a sieve, he actually solves a lot on his own: puck handling on dump ins, his vision and vocal instruction back there helps ease the load on his defense.
They need to dial back on forward blitzes and swing at least 1 F lower to support the breakout, until they can improve personnel (definitely needs it). Once they solve this key link in their play chain, a lot of other things will sort themselves out.