It depends on the game. I don't know alot about the ae200, but if you set the xbox to 16:9 and then go into a game, let's say Halo, and halo is actually 4:3, then the only way you would get 16:9 on the pj, is if you were to manually tell it to goto 16:9, which you would then end up with squished image. Now you pj probably remebers its settings for each input.
For example, on my VT45, my xbox is hooked through component, and I have it set for 16:9 as well my PJ is set to that mode as well, when I put a game in that is 4:3, it automatically switches to that mode, and then back again if I'm at the Xbox menu, or if I want to play a 4:3 game in 16:9 then I have to tell my pj to do that.
When I switch to svideo for my dish, it remembers that I had it set to the 4:3 mode, but If I were to tell my pj to go 16:9 then it would remember that next time I switched to svideo.
so I'm guessing that your AE200 does the same, and the last time you had svideo on, it was already in 4:3 mode.