For two more anecdotes, my coworker and I have had similar experiences. My RSI isn't entirely gone, but I had to take a long break from pushups because of an injury. I'm able to start doing them again so I should get to it, because I had a significant reduction in symptoms after only a week or so of pushups.

This site might seem a little spammy, but its methodology for figuring out how many to start with and at what rate to increase the # of pushups was a big help for me. I started at about 3 pushups and even after a long break due to the injury I can do 15, which is saying a lot since I am completely out of shape!