The "truth" has to do with the way one views reality, and to Alpha/Beta, Fe is more important than Te. Te "truth" as Gamma/Delta knows it is, from a Fe perspective, ignoring what's important, which may interpreted as hiding the truth.
I've learned this to some extent dealing with an INFp. She'll say that something happened when it didn't, and I've come to see that from her perspective, she's telling "the truth" as she knows it. To her, adding details or fabricating events isn't a big deal if it helps communicate what she wants to communicate. When I give her the objective facts but don't allow my feelings to show in what I'm saying, to her I am the one who's being deceitful. To me, my emotions are not important to the discussion and I see no reason why I should be expected to express them.
I realize that this is most likely a biased view. Feel welcome to offer feedback on my perspective of this subject and describe your own perspectives. (Let the bitching commence... )
disclaimer: I'm not saying that all Fe types blatantly lie.