Oh and David, my name is Ted. I put myself as an IN(t)FJ because when I was around 12, I started to give up on emotions for decision making. I would override my value system and focus myself to look at the logic of things. It's really when I began to develop my Ti, but I developed it in a negative way that caused me to totally disregard an important part of myself.
This would cause me to test as an INTP by the time I was in my early 20's.
Fe was always there, just I ignored it to the best of my ability. Other people who knew me often thought I looked angry though. I had got to the point where very often I had no idea how I was feeling.
Last few years, while still believing myself to be an INTP, I went on this quest to get in touch with my Fe side, since that is the inferior of an INTP. Then a guy pointed out I use Ni and not Ne. He was right, and since exploring my Fe side, it has made leaps and bounds to the point I don't think it would qualify as an inferior function anymore.
So you're right, a person can't be Ni Ti Fe Se. What has happened is my Fe *must* be run through my Ti most of the time, to make sure I am acting appropriately in different situations. This gives me a more stern, and academic attitude. I behave remarkably like an INTP, and not so much like an INFJ. After being on the INTP forum for a couple years, I realized I was subtly different than most on there, and I just figured I was a screwed up INTP. Nope, INFJ is the answer.