IANAL, but most US broadcasters add a written statement along the following lines ..
Broadcasts may not be copied whole or in part with out the expressed permission of (the owner of the property).
.. and/or include a broadcast flag in the stream.
One frame (a picture) would be considered "in part". If you intend on doing this, I would make sure I vetted your idea through a lawyer first.
Paramount seems pretty unhappy with frame by frame tweets of top gun.