In friendly online games, I have seen that if i press print screen, and i go to windows to paste the screenshot on Paint, when i come back to NBA Live 07, connection has been lost... so i think i have one solution for this problem:
In Pro Evolution Soccer Online leagues where I play, we use Fraps to capture the goals' video from the highlights replays that are shown at the end of the game... but Fraps can also capture screenshots in game, pressing a preconfigured key, and this program saves the screenshots in the folder that you have previously configurated...
For this reason, until a save stats patch is released, i recommend Fraps for capturing stats screenshots without having to leave stats screen of the game.
Here you have a link to a fraps tutorial I made on the spanish Pro Evolution Soccer league in which i am admin, as soon as i can, if you find it useful, i will make an english version to this tutorial...
http://www.pes4animersion.net/tutorial2.htm
Respect!!!