Representative Max Miller of Ohio categorically denied the accusations against him in a roughly 20-minute livestream that he had previewed as a “special announcement.”

The policies that May Mailman has helped devise have sent shock waves through higher education, dividing faculty and alarming some students who see an effort to silence dissent.

The fabricated video of Matthew Miller, the State Department spokesman, had telltale clues of manipulation. The lip sync was off, and Mr. Miller’s shirt and tie changed color midway through.