Is there a way to get a screenshot / snapshot of a movie purchased on iTunes? Using ⌘Shift3 or ⌘Shift4 won't work -- it will capture a grey window. (I think it is due to the video being displayed using the video card's video buffer).

I think one way is to use an iPad and play the movie and take a screenshot by the Home and Power button together, but other than that, is there a way to take it on the Mac, without installing any additional program?
You can't take a screenshot of a protected video with the stock Mac tools.  Apple has built-in protection to prevent this from happening (if the video is not protected, then it's ok to take a screenshot).

The only way you'll be able to do this is to use a third-party video player, like VLC, or a third-party image capture, like SnapNDrag.