Bloody silly assertion. It's obvious that St. Luke interviewed the Virgin Mary--Holy Tradition says that he even "wrote" several icons of her from life, one, a small icon carved in mastic overlaid on wood, is preserved in the Monastery of Simonas Petras on Mount Athos.
Now it is true that the oldest extant manuscript of the Gospels date to about 200 A.D.
The critical date is 49 AD, since Claudius expelled all Jews from Rome (Christian and non-Christian Jews) at that date. John Mark was a Jew so he hardly stayed behind if Peter was expelled at this time. The earliest time for their return was after Claudius died in 54 AD. Apparently the Gospel of Mark is from this period and very likely written in Rome, or at least for Jewish-diaspora Latin speakers since it has so many Latinisms in the text; and was very probably sourced from Pater, for whom Mark acted as scribe.
I am by no means an expert on these details. It's just what I've read.