If you take a screen grab of the player, those elements will be on top of your video still frame. The problem I was having is this: If you pause the video and use the left/right arrow keys to move the playhead exactly to the frame you want, the player controls are still showing over the video (in addition to the video title bar/window chrome. However, I'm glad I finally figured out how I can grab one frame from a movie in QuickTime Player X. but there were also a ton of features removed (like being able to set advanced export options, save a movie as images, and do some other more advanced edits/exports.
There are many things to like about QuickTime X, and many improvements were included over QuickTime Pro 7. In recent versions, to grab a frame, do the following:
Update: More recent versions of QuickTime Player have the ability to copy frames of the video by using 'Command + C'.