On the other hand, Hotmail being run on Windows shows that MS believes the server editions of Windows to be stable enough for their own use, implying that it should be stable enough for whatever you might need to do, too. Keeping customers from switching to *nix is of immense value to them.
Sure they did. Microsoft's internal infrastructure and corporate culture is very Windows-centric (obviously). Maintaining a totally alien FreeBSD-based infrastructure for Hotmail would be very expensive in the long run, and make integration with the rest of MSN prohibitively difficult. Which is to say, it would directly interfere with one of the main goals of the acquisition in the first place.
They would have needed to vastly overhaul and rebuild the infrastructure multiple times to scale the site and add new features, anyway. The question is just whether to do those overhauls as part of a transition to Windows or not -- and I think the answer is that moving to Windows obviously makes sense in the long run, even disregarding the non-zero PR benefits.
Actually they got a huge benefit. They had internal users doing a high-volume stress test on Windows and associated middleware, so a lot of bugs got found and fixed. The products now are noticeably more reliable.