I suspect there's a strong parallel between Ti and Fi, here: Fi gets an internal sense that something is "wrong" or "right", but not in a logical or objective sense.
But there is another piece of the function pairing that is more conscious, and which I believe contributes to mistyping of oneself and others. The dom and aux functions work as a pair, and, I believe, the tert and inf functions work as a pair. As an INTJ, I think abstractly (Ni) about objective things (Te), but my feelings (Fi) seem more attached to immediate environment and sensations (Se).
This ends up messing up typing because, for example, NiTe and TiNe often seem to do the same kinds of things in the same kinds of ways, and the differences come out only when you watch the different types argue about something abstract and technically complex. For example, INTJs can easily become convinced that they can "do Ti" too, especially if they take one of Nardi's cognitive function tests. Similarly, an ENTP might easily believe that he can "do Ni" as well as Ne: he just focuses more on getting the right answer. But really, that's just Ti, not Ni.
I think we can feel the difference between the e and the i, but we don't so easily notice that we're switching between the Ti and the Ne (or the Ni and the Te) when we switch between the i and the e.