Exploring the Shakeout website some more, it's interesting that Doug Copp and his "triangle of life" concept seems to be visibly and thoroughly rejected and he is vilified as a fraud now (apparently a false 9/11 Ground Zero hero who then claimed disability from the compensation fund).
I haven't heard Doug Copp mentioned in many years. I ran across his ideas quite a while ago and they made sense to me, although I realized that his ideas were based on buildings that were not built to "earthquake standards". Still, I thought it was a useful concept to keep in mind.
If you were somehow in a building that you sensed was collapsing, then it would make sense to seek shelter next to something large and sturdy and get out from under anything that would pancake right on top of you. At the time, memories of those poor souls who were crushed on the Cypress section of the I-880 during Loma Prieta were still fresh in my mind. Arguably, those people would have survived if they had been crouched next to their cars rather than sitting in them, but that's a hypothetical situation that we'll never resolve. That Haitian school collapse the other day is another example where being next to something would have been safer than under something (although this case doesn't involve an earthquake).
As far as the official line in what to do in an earthquake here in the US or anywhere with reasonably strong construction--
drop, cover, and hold on is still the rule. When buildings are strong enough, most injuries/deaths are due to getting hit by falling objects, particularly as people try to run outside during the shaking, or else getting their hands/feet cut on broken glass. Stay put, protect yourself from falling objects until the shaking subsides.