Paralyzed by fear...

What does it mean to be paralyzed by fear?
I've thought much on the subject, and I don't agree with the wording of this phrase.
To be paralyzed by fear suggests the inability to move when afraid. However, this is contrary to the "Fight or flight" response that comes so naturally to humans.
I suggest that we are not paralyzed BECAUSE of fear, but IN SPITE of it. If we are truly so plagued by fear that our only WANT is to run, then our inability to move would be a NEED to stay and fight.
I have seen many people afraid, and the ones who don't scream and run always have a look of inner struggle in their eyes.