This short clip about Princess Berenice, the mistress of the Roman emperor Titus, and her supposed identity with Veronica of the Stations of the Cross, is from the bonus materials included with the Caesar's Messiah documentary by Joseph Atwill.
Note: Atwill's 2011 book, Caesar's Messiah: The Roman Conspiracy to Invent Jesus, argues that the Christian religion was created by the Flavian emperors as counter-propaganda to the anti-Roman Jewish Messianism which was causing so much trouble in Palestine at the time.
Atwill's theories are interesting, I guess, but they tend to fall apart when you get into the details. For instance, in this particular case there doesn't seem to be any connection between the Saint Veronica of Catholic tradition and Berenice, Titus' mistress, other than their names. Veronica is the Latin version of Berenice (or Bernice -- I'm not sure how it's supposed to be spelled), but the fact that the names are the same doesn't really mean anything.
Atwill's argument assumes that the figure of Veronica existed in Christianity when the religion was first created (supposedly) by the Flavians. After all, if Veronica was actually Berenice, Titus' mistress, and the whole point of including her was to plant a clue as to the true origins of the religion, then she must have been inserted into Christianity during the reign of the Flavians.
Unfortunately for Atwill's argument, there is no mention of Veronica in the Gospels--not according to the Catholic Encyclopedia at least--and the Stations of the Cross tradition seems to have originated during the Middle Ages, perhaps during the Crusades. The whole story is apparently a medieval legend and it has a lot of similarities with the story of the Shroud of Turin.
In the Stations of the Cross tradition, a woman later identified as Saint Veronica gave Jesus her veil to wipe his face while he was being led off to execution. When he gave it back to her, the image of his face had been left imprinted on the veil. The "Veil of Veronica" was supposed to have healing powers like the Shroud of Turin, but the legend apparently never caught on in a big way and a lot of Catholics don't believe the story's authentic.
If the legend originated during the Crusades, the Veil of Veronica was probably just another pious fraud invented by the Crusaders, who brought back all sorts of "holy relics" in order to make a profit off the gullible and superstitious peasants back in Europe.
Atwill's theory that Veronica refers to Titus' mistress collapses entirely if the figure of St. Veronica was created during the Middle Ages, and that seems to be exactly what happened.
The legend of Veronica is based on a miracle reported in the gospel of Luke (and Matthew?) where an unnamed woman "was healed by touching the hem of Jesus’s garment (Luke 8:43–48)..." (Wikipedia) This woman was "later identified as Veronica by the aprocryphal Acts of Pilate," thought to have been written around the middle of the 4th century AD, i.e., almost 300 years after the death of Domitian, the last Flavian emperor.
The church historian Eusebius (260/265 – 339/340 AD) described the origins of the legend of Veronica. Interestingly, she was originally only called Veronica in the East while she was known by a completely different name in the West:
"Eusebius in his Historia Ecclesiastica (vii 18) tells how at Caesarea Philippi lived the woman whom Christ healed of an issue of blood (Matthew 9:20-22). Legend was not long in providing the woman of the Gospel with a name. In the West she was identified with Martha of Bethany; in the East she was called Berenike, or Beronike, the name appearing in as early a work as the 'Acta Pilati', the most ancient form of which goes back to the fourth century." Source: Encyclopedia Britannica (quoted by Wikipedia).
Note: It's unclear, at least to me, how the bleeding woman healed by Jesus morphed into the Veronica who wiped off his sweat and blood with her veil, but we're dealing with a muddled tradition here that evolved over the centuries.
As for the Stations of the Cross ritual, it apparently originated with the pilgrimages to Jerusalem. According to Wikipedia, "The earliest use of the word 'stations', as applied to the accustomed halting-places in the Via Sacra [the route the pilgrims followed] at Jerusalem, occurs in the narrative of an English pilgrim, William Wey, who visited the Holy Land in the mid-15th century, and described pilgrims following the footsteps of Christ to the cross."
Conclusion: I don't see how St. Veronica could actually be Berenice, Titus' mistress, if the woman in question wasn't even given a name until the Acts of Pilate were written some 300 years after the death of the last Flavian emperor. If Atwill is aware of some earlier documents, he should cite them. Otherwise, his whole argument boils down to the fact that the names are the same. This doesn't mean much, however. The Oxford Classical Dictionary (OCD, 3rd ed. revised) lists five different Berenices, so it wasn't exactly an unusual name in the ancient world.
The OCD does verify that Berenice, the niece and later the wife of Herod, king of Chalcis., was Titus' mistress before he became emperor. "Titus fell in love with her while he was in Judea (67-70), and when she visited Rome with [her father] Agrippa, [Titus] openly lived with her, perhaps for some years. He deferred, however, to public opinion and did not marry her, and on his accession [79 AD], he dismissed her with regret on both sides and ignored her when she visited Rome again."