Maybe streamplay is the reason for that rumor about the console requiring a constant internet connection? We all just assumed it was to verify the games and to combat piracy, but maybe the real version is its literally required to stream the game for you to play it?
But I think to pull that off you would still need to have some basic framework of the game downloaded and pre-installed, but this would still take up a lot less space than having the entire game on the hard drive. Basically, you would download and install the skeleton of the game which might be like 1/10th of the total size, and then you would stream play the guts.
If it was done like that then a very limited amount of on board flash storage should be more than adequate. A fraction of the game would be installed locally of course, but the majority of the game would reside in cloud land.