I've heard a much different story regarding "Digital," but it wasn't where MS-DOS originated, but how IBM became involved with Microsoft. It wasn't "DEC" (Digital Equipment Corp) but "DR," "Digital Research." And MS-DOS wasn't based on it, it was a competitor. IBM wanted to buy an OS for its new computer, and the owners of DR were too busy to see the IBM reps, on vacation, or refused to sign the NDR, depending on which story you listen to.
And not if it's running Linux, in which case quite a bit was was influenced by Andrew Tannenbaum.
Though you may be more correct that you realize. One of the chief architects of Windows NT, Dave Cutter, was was hired away from DEC, who was behind the VAX11/780 and VMS.
Mark