From all the research that I've done, I'm fairly certain that I'm almost unique.
I (finally) got around to changing my password and logging in to PSN through my PSP today, and I promptly followed to download my Welcome Back games. After selecting "Free Game 1", I got an error, ignored it (yeah, I shouldn't have) and selected "Get Now". So I got Free Game 1. I didn't, however, get to select which game I wanted.
After looking around a bit, I found out that I could select which game to download via Account Management > Transaction Management > Services List > SCEA or something similar. I followed the menus and got to a page where I have Free Game 1 and Free Game 2, both NOT used (Times Used says "0" pretty clearly, and Times Left says "1"). Upon attempting to select either one of them, I found out I couldn't. There was nothing mapped to the X button.
So I ask you: how can I select the games I'd like to download through the Welcome Back program?