ah-ha!

Glancing at Osborn's book on google books (just to see what I'm getting!), I think it already looks promising. This is the opening:

Clement was a traveller, always moving on. He invites Greeks to desert to God's side and to enjoy the danger of change [...]. In his quest for knowledge, he left home and travelled to teachers around the eastern Mediterranean, moving from Italy to Egypt.

Of these [teachers], one, an Ionian, lived in Greece, two others who came from Coele-Syria and Egypt respectively were in Magna Graecia. Others were in the east - one was from Assyria, and the other a Hebrew from Palestine. I found the last of them where he was hiding in Egypt. Here I came to rest. He was a real Sicilian bee who drew from the flowers of the apostolic and prophetic meadow and who engendered a purity of knowledge in the soul of his hearers.

He remained in Alexandria until in 202 persecution drove him to Palestine, where he died.

So Clement himself was a traveller and an exile. I guess we should have known!