THE NINTH DOCTOR WAS A BUST!

At some point in those adventures which were unseen by the audience in the Trueniverse*, the Ninth Incarnation of the Doctor must have become famous - or infamous - in Ancient Rome.

Why?  Because there seems to be statuary evidence to that fact:

But this being the Toobworld Dynamic, I'd like to make another suggestion.....

These busts were made on the planet 892-IV, which had a Roman Empire-styled civilization but on a 20th Century level.

'STAR TREK'

"Bread & Circuses"

The Doctor, Rose and Captain Jack would have arrived there after the Enterprise departed.  Because surely the Doctor would have been able to right the situation before any more crew members of the Beagle were killed in the arena.

BCnU!

* These would have taken place at some point between "The Doctor Dances" and "Boom Town" - we see the Doctor, Rose, and Jack recounting some of their adventures to Mickey......