This argument makes little sense: that "vice versa" is wholly unsubstantiated and without it the rest collapses. Making Linux binaries work on NT (which already has a subsystem concept; Interix proved that this could be done) in a way where they interact little with the Windows desktop, and making not just NT binaries but Win32 binaries work smoothly on Linux, are almost entirely unrelated problems.
It is true that MS owns the code necessary to make this happen, that WINE is an existence proof that it can be done shockingly well even without that code, and that there is both code and expertise at MS for stuffing Linux concepts and NT concepts in the same kernel. But that's about it.