Although considering the Twin Towers it may just collapse, not actually fall over.
I have to think that the straight up and downness is the gravitational backbone that holds the thing up, and if you lean it too much the whole structure will just unspool itself. It's not a tree -- it doesn't have a lot of lateral stability.
But I am not a materials scientist, I just built a lot of sandcastles.
Reminds me of the only earthquake I have ever been in. I was in a building with enormously wide and tall floor to ceiling windows, and I happened to be looking at one when it hit. It liquified, like the Star Gate; it was a pool at a 90 degree angle from the ground for a moment. And then it solidified again. But it's not as if it would have cracked and fallen in, it would have just showered like water. That's what I think would happen to that tower if it lost its vertical structural integrity -- it would effectively just be a tower of sandy Rice Krispies, and it would pour, not fall.