The precise question the Supreme Court agreed to hear in the case involving First Choice Women’s Resource Centers, which runs five centers that say they “offer free medical services and material support to women facing unplanned pregnancies,” is a narrow one.

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.

In the trial’s first weeks, prosecutors have played their strongest card: testimony about the sordid stories that Donald J. Trump is accused of covering up.