[Canard]

"This woman, and the queen of all people"

The queen has nothing to do with this broadcast.

[Nathan Zachary]

"A Muslim woman in a full-face veil went head-to-head on television with Queen Elizabeth II, delivering an alternative Christmas Day message"

I took that as meaning 'appearing with' as in on the same program.
That's what "head to head" usually means. Perhaps it should have been written "appeared simultaneously on television with QE2"