I have encountered this as well and found that if you place swtor in windowed mode the printscreen function will work correctly even if the game is running. So for instances where you are working on non-swtor screen captures, the game will not interfere with what you are doing.
In relation to use the snipping tool, it does have an option to do a full screen snip if you do not wish to have the game in windowed mode. To get rid of that red border you can open the snipping tool, go to options and uncheck the box marked "show selection ink after snips are captured".
I hope that helps.
I run only in Windowed mode and using Alt+Printscreen to grab a selected non-swtor window does nothing.
Thanks for the suggestion with the snipping tool. I'll try that in the meantime.
I'm running Vista 64 if that helps.
Edit: I also tried just using Printscreen with a non-swtor window, and that did nothing as well. Nothing in my clipboard and nothing in the screenshot folder.