"Purely Roman"? No. While you are correct that panel painting started earlier than the mummy portraits, as I said in my article, it was both a Greek and Roman art. The Fayum portraits started during the Ptolemaic (Graeco-Egyptian) rule and in a place where many Greeks and mixed Graeco-Egyptians lived. Plus in the eastern Mediterranean at this time many of the artisans and craftsmen were Greek. In the cosmopolitan world of the eastern Mediterranean, with its constant interaction between cultures, it's hard to say anything is "purely" from one civilization.

Sorry, but maybe I was not clear: The tradition of portraits are certainly
commune to ancient mediterranean civilisations, but the particular kind of
portraits that you've show in the article, its style, and - if I remember right
- its times, are "purely" roman. I invite you to watching the roman portraits
of Pompei and Rome, from the same period, and do a comparison. Anyhow, I know the portraits showed in the article; those appear in the titles of roman
history of art.