(Replying to myself.)
I've tested running the Arduino SDK 1.5.1r2 in Windows 8 Pro in a Parallels VM with the same OSX 10.8.2 as host OS. Arduino in Windows is able to talk and upload sketches to Due without any problems (after disabling drivers signatures in Win8). So, the problems seems really to be with how OSX handles serial ports and how the Arduino SDK expects them to work.
Anybody have any ideas how to resolve this?