Note: M-W says 'pseudo' is from Late Latin.

Every other source I've seen says it's Greek. Seems like an obvious mistake, but I suppose it's possible that Greek was it might have come to us from through some circuitous route.

It's Greek. You don't get ps word initially in Latin. It may have come through Latin as many a word did. There's a play by Plautus called Pseudolus. The title character is a smart slave. This is the basis for the Zero Mostel character in the movie of the Sondheim musical A Funny Thing Happened on the Way to the Forum. I have a dictionary of Late Latin; I'll take a look-see.

??
pseudo-
[ME, fr. LL, fr. Gk, fr. pseudes, fr. pseudesthai to lie] [MWCD-10]

Cf. post-classical Latin pseudo- [OED2]

OK, I've look it up in Alexander Souter's A Glossary of Later Latin to 600 AD. There's about 1 1/3 columns of words beginnig in pseudo-, e.g., pseudoapostolus 'false apostle' to pseudothyrum 'false (secret) door'. Name that keeps cropping up is [Sophronius Eusebius] Hier[onymus] aka Jerome, he of the Vulgate. So, it became a kind of prefix with the Church Fathers.