I don't think this is true.
Blood to the face is supplied by branches of the carotid arteries but all blood that goes to the face will return to the heart then the lungs and then the heart again before going anywhere else.
I'd never heard of this before. I had read that it is possible for infection from the face and upper jaw to track to the the brain, so maybe there is some venous return from the face via the brain.
https://en.wikipedia.org/wiki/Danger_triangle_of_the_face