I paid the fee and got the AE7 tutorial and watched in amazement as this guy takes some really shakey footage and smooths it right out.

WONDERFUL!

I thought, This will make my hand-held / fig-rig shots look as smooth as a $5k dolly rig.

Right?

Or is there something I'm missing?

Don't forget you'll have to contend with your outside borders moving around. Also, I've noticed that if my shutter speed is slowish the footage will appear to lose focus because of the motion blur even if it's stabilized. Using a faster shutter can solve that though.

Depending on your shot, you could also have paralax issues to contend with.
In most situations, the 2D movement of a point in the distance moves more slowly through the frame than a point that is close to the camera.

Since the smoothing done in AE is a 2D effect, you can run into situations where the correction won't "look right" because, even if you smooth a close obect, the distance will still be shaky (or even get shaky-er!) ... or ... you smooth out based on a distant reference and something near the camera still looks shaky.

This effect can help in some situations, especially if you use a less-than-solid dolly/crane and just need to smooth it a bit, but I wouldn't expect it to be able to consistantly make a hand held (even fig-rig-hand held) shots look just like they would using a solid dolly system.

What video is this? Who hosts? Is it Andrew Kramer? I must say I'm a huge fan of his.