The rumor mill has it that they tried real stick physics at one point, and it just became unworkable. I can see that being the case, as with the way the AI currently moves and behaves, there is nothing like sticks hitting players or other equipment, even the boards don't affect it.
Part of it is likely an issue with clipping of animations, where the animation just can't be forced to 'look' like the player is along the boards (For example, in real life when a guy's on the boards with the puck, they've got their stick up against their body at a really steep angle, limiting their ability to pass and move the puck.
Messed that up. Here's Oshie on the boards. He's being pressured from behind, and in real life, his movement is restricted. It's a huge part of boxing players out and limiting their effectiveness. In real life, he wouldn't be able to just skate back towards the net, because he's got someone pushing from behind, and limited space to move his stick, and therefore the puck.
In game however, you're not limited like this. At worst you get put into the awful boardplay animations, but even then the AI can still make laser passes to the slot with their feet. Notice that the guy pushing is getting support from another player who's watching for the puck, and Oshie is forced to jostle for position before getting the puck on his stick. Even if he does get the blade of his stick on the puck, he still won't be able to make the super precise passes that we see in game. His best bet will be to get support on either his right or left, or manage to kick the puck one way, and duck out of the pressure, maybe being tied up and held, resulting in a penalty.
In game, it doesn't work well at all. Guys checked towards the boards too often bounce off of the check, and easily fire crisp no-look passes into the net off of their backhand (it would be cool if stick curve and passing skill better affected this). It's another in my long series of constant whining about defense. Playing defense is just hampered by the AI's ability to do more than they should be able to, and your ability to play solid defense with the nerfed toolset available to you.