Doesn't take much to lose your balance. Especially from an unsuspected cross-check
Sure but this d man doesn't look like he is braced for any contact. I don't believe this is an icing so it is a live puck. Watch the clip:
The d man cuts across the ice to get to the puck in the corner. With his peripheral vision and on ice awareness he should be aware that two Wheat Kings players are coming hard on the forecheck and only one of them has their path to the puck obstructed by a teammate. The forecheckers are flying in and only a few strides away so even if he successfully retrieves the puck it is highly likely that he gets hit. I don't see him preparing himself to get hit at all. If he did then I don't think that crosscheck would have knocked him over if he was bracing himself for a hit.
The only other explanation that comes to mind is that the D man is completely unaware that Greig is on the ice and flying in on the forecheck. He skates to get the puck and notices that while there is a Wheat Kings player coming in on the forecheck along the wing that his teammate is obstructing his path. As he goes to retrieve the puck maybe he takes a slight glance toward the forechecker and notices him curl back and thinks he is about to make a change. He completely relaxes thinking there is no pressure on him and goes to retrieve the puck without bracing for any contact. He would be unaware that Greig is flying in on him and about to hit him and then when Greig crosschecks him he goes flying into the boards because he isn't expecting any contact.
If the puck was live then that would be a poor read by the d man if he was completely unaware that Greig was flying in on him. Greig made a dangerous play with that crosscheck, but even if he didn't if that d man was unaware he was there then he would have left himself vulnerable to get killed by a hit.