Left Shift and Left Command combination yields only Left Command; other shift command combos work fine
I'm posting the non-answer of "I reinstalled OSX and upgraded to Maverick from Lion, and it now works" because, well, it now works. Unfortunately I don't know what were the actual reasons it broken and then un-broken. I am sorry to anyone whom this question didn't help at all.

If anyone else comes up with a reasonable explanation I'll mark them as the answer instead.