Yes, the way his hand is positioned, it would not have worked if they had wanted to make it hold the wooden stick. They'd have needed to edit the hand too much and it would have likely been noticeable / even weirder.
Probably they decided: f*ck it, let them grab it however they want. Maybe it'll even become a thing.
And it looks like it worked, since we are talking about it and spreading the ad. Smart advertising, imho.