The chronology I've read is that Gates purchased the original MS-DOS for a song and a dance. I believe it was QDOS from Seattle Computer Products back in 1981. I wanna say it was in the $5k range. Don't recall exactly.
That sounds as reasonable as anything. I guess everyone (even Deckies) wants to think they’re part of the legacy. I used to think the dec connection - whatever it is - was a stretch but he did spend some time in the area and back then, DEC was very happening.