Moreover, I'm unfamiliar with theory regarding NaN and NA.
I don't think there is really a theory with regards to NA. NAN is part of the IEEE 754 floating point standard, and has set rules that Octave tries to follow (in addition. To trying to follow MATLAB compatibility). NA on the other hand, is to my knowledge primarily used as a particular error value in MS Excel, and I don't believe it's defined in any numerical standard. I don't believe Matlab handles NA as a data type either.
So, unless it's been defined elsewhere, I think the properties you're examining may be unique to octave. Will probably need someone involved in early implementation to comment on the "why"