That's interesting; I don't see anything in the OP signifying that you only wanted MBTI analysis. If you didn't want to discuss Jungian functions, I find it odd that you used them freely in your responses to other posts here. If you stick strictly to MBTI, Te, Ti, etc. are meaningless terms because MBTI only deals with E, I, N, S, F, T, P and J as separate and distinct concepts. There's no sub-classification of S, N, T or F.
You've got it backwards. The MBTI types were extrapolated from Jung's functions, not the other way around. MBTI doesn't actually discuss directional functions at all--it doesn't differentiate between Fe and Fi; both are just condensed into "F." Therefore, if you're discussing Fe, Fi, Te, etc., you are using Jungian terms.
Nobody can prove anybody wrong about the types of anyone, so I don't understand why you keep asking for that. Typology, since it is not testable or empirically verifiable, operates on inductive reasoning--the best you can do is make a "strong" argument that x person is y type; you cannot evaluate subjective analysis in terms of deductive reasoning. There is no such thing as a truly "correct" or "incorrect" typing, only "strong" or "weak" arguments for types (which are ultimately subjective anyway.)
Aside from that, though, I think you've missed my point about Fe vs. Te. Having strong family values doesn't necessarily indicate Fe use; having a conception of morality based on an external standard does.
So one could have strong family values based on Fe--if his idea of ethics is based on an external standard and that external standard says that family values are important.
Or one could have strong family values based on Fi, if his idea of ethics is personal and internal, and he feels it's important to support his family structure.
Or one could have strong family values based on Te, if his idea of logic comes from an external standard and he sees that keeping a family together is an objectively effective method of reaching whatever goals he has.
Or one could have strong family values based on Ti, if his idea of logic is personal and internal and he believes that it's logically consistent to support his family structure.
etc., etc...you're still defining functions according to displayed behavior, but functions don't do that. That's what MBTI's basic four-dichotomy sliding scale system is for. Observing and categorizing obvious surface behaviors--the what, not the why.
Functions are more difficult because they describe fundamental components of value systems--if we say someone uses Fe, all we're saying is that he bases his concept of ethics on some external standard. This may (and frequently does) result in "strong family values", but some Fe users do not have strong family values. The defining characteristic of Fe is that it motivates people to define morality according to an objective external standard--the why, not the what.
If you're not interested in discussing functional value systems/would prefer to discuss only MBTI, that's fine, but it does make it confusing when you use terms like Te and Fe in your analysis. MBTI doesn't encompass these terms at all.