What you have to understand is that statistically the models are very similar (you can compress them both into one unified model that does what both of them do quite well). However, the ways the models are constructed makes them useful for different things. The Big 5 is primarily useful for academics, and the MBTI is primarily useful for the rest of us.
If you are a logical positivist and scientific realist you'll never be able to grok this. As a utilitarian I understand that science is the process of making something that does something you want done.
I think I grok that some simplifications are more useful and teachable than others, and that it's possible to accomplish useful things by simplifying (and also by misleading). But I don't think you have to be a hardcore logical positivist to think these are distinct notions from "validity". My impression is that you have psychological or statistical training, so when you used the word in your original comment I assume you know what it meant.
If you are a logical positivist and scientific realist you'll never be able to grok this. As a utilitarian I understand that science is the process of making something that does something you want done.