It’s kinda true; I’ve certainly seen the number cited multiple times—it was the guess around 1900, for scholars saying there was no point even attempting a dictionary of all of Greek, to rival the Thesaurus Linguae Latinae.
I work at the Thesaurus Linguae Graecae, although it is not a dictionary per se, but an online lemmatised corpus. As I wrote in How much writing from ancient Greece is preserved? , we know how many words there are of Ancient Greek texts—our collection is reasonably complete up to Middle Byzantium.
I think the 10 times as much figure is too much: it means excluding Mediaeval Latin (which you can do), but not excluding Mediaeval Greek (which I would start as early as the Church Fathers).
Some possible reasons:
- Lots of scientific/scholarly texts in Hellenistic Greek. Galen alone accounts for 3 million words.
- Huge amounts of Christian theological works, which the monk copyists preserved assiduously.
- A much longer literary tradition.
- A lot more people writing to begin with, I suspect.
But if you let Mediaeval Latin in, the scores balance.