"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.