Brian I've seen the 2-2 as a response to the 3-3 invasion. I haven't been able to figure out how to get life on the invasion as a response to this move. I've even used it in a couple of games myself with great success. Mind you, that I'm only a 25k and the highest level I've used this against is a 19k. There very well could be something I'm missing.
Phelan: Position search gives me two pages with this 2-2 counterinvasion: 33PointInvasion/Discussion and BQM332 The key to living in the corner in this position is not to go straight for the capture. Instead, go for space, and extend along the top or the side (a or b). Then it will be Black that will be in trouble to live (or make a KillingShape) with . If he does live, he'll have made his 4-4 stone weak.