Mega stone age bump, but...
Just got this ad again (advertising the snowball game) and was hoping to find the 5th prop. It wasn't there sadly, however, on a whim I decided to go through the Razr prop. After answering the questions, I picked the purple one as I knew I didn't have it. It let me right into download. I tried again for the white one, but it popped up the screen about downloading the purple again.
So it seems the information held has reset allowing a second download. And if you really want them all, the second controller trick should work. No idea what causes the reset (a day, a week, year change, etc.) but still a heads up if anyone wants a second color. Oh, and for those that didn't get it beforehand.