You didn't understand. There is no redirect. The "redirect" consists of loading the target page in a window-filling frameset. As such, it has nothing to do with HTTP and consequently isn't handled by the LWP modules.
Now, that all makes sense. I didn't notice it until you mentioned the frameset, but another part of the code that handles framesets should have handled it correctly but failed bec of a bug with trailing slashes (see my other post) that I have fixed since. Now, it all works. Thanks for the jogging of my mind :)