Mach is not a Unix kernel and the Mach interfaces percolate up to the higher levels for many tasks which aren't covered by the POSIX layers.
The bigger difference, though, is higher up. While you certainly can compile POSIX code on OS X, most of the applications which people run use Cocoa and that owes far more to the NextStep side of its lineage than the Unix bits.
The better comparison might have been Win32 rather than DOS, where most of the interfaces were designed by the Win95 developers even though they were also implemented on top of the NT kernel. I've often wondered how much better things would have been in the late 90s/early 200s if David Cutler's team had been able to get the Win95 team to follow their generally much better instincts rather than the other way around. If nothing else, they wouldn't have needed to spend a decade duct-taping security onto a single-user design.