There seems to be an idea that "Fi reads people" (as if it's a tool...). I don't think this is quite how it works.
No, it really goes after the "tone" of people. The ability to sense "fake" is really the ability to sense when something doesn't match up. It doesn't mean something is wrong, but it does mean that something isn't quite right.
An xxFP has perceptions via Pe - Se types often note tangible indicators (ie. body language) & Ne types work with those intangible "vibes".
What Fi does is make the judgment call based on an understanding of how people work. This is an understanding that has been refined in the mind via exploration of the self (which is used as a sort of prototype for understanding people), & in the case of NFPs, via invisible patterns observed in people over time. I admit that "figuring people out" is a little game I play with myself, and practice tends to improve such "skills" (oh yes, I am psychoanalyzing you!).
Yes, this does seem to be a trait of the FP types - an overall desire to evaluate what a person is really like. On the xNFP side, I note that ENFPs are particularly good at making snap observations along these lines, while INFPs tend to withhold a "final" judgement.
Most Feeling types will tell you they feel they understand people well or have an interest in doing so, but to me, F-dom with aux iNtuition (INFPs & ENFJs) are more preoccupied with refining their understanding to be used on a larger scale. With F-dom, the primary focus of their mind is what things mean & what is their significance in in terms of people, and then iNtuition aids in seeing what is not immediately apparent on the surface. From an INFP perspective, you form general concepts to work off of, and then you can make some pretty dead on inferences about how people are & why they are that way. This can occasionally result in being dead wrong when projection is involved (and projection is more often an issue of Pe for xxFPs than Fi, IMO), but that doesn't mean it's a total crapshoot. You're seeking to make sense of people in emotional terms (which is not logical, but it has a sort of consistency to it still), so it's not just trusting a gut feeling (which may be more true of P-dom).
What I notice with xSFPs is a heavier reliance on first-hand experience. Projection occurs when their experience is limited & they use this limited knowledge to draw a conclusion & don't consider other possibilities (whereas a Ne type may invent possibilities that don't exist). However, they also work with more concrete, factual information, which has obvious advantages. I see that with SFs, period. My ISFJ mom can recall physical things about people that lead her to the same conclusion I get, but I can't connect it to anything solid. I just "know", and I make sense of this knowing using my general understanding of how people work.
Oh, and I think I should add that xxFPs are probably more preoccupied with noting and annoyed when they suspect that someone is being "fake", just due to the nature of their own mindset.
Good synopsis.
There is an interesting aspect of Nardi's research, where there's a missing piece of the symmetry in terms of the "Intuitive listening" section of the brain. All of the FPs use this section a lot. That's the main consistency. A corollary consistency is that the Ti doms don't use it much at all. In between, it's a bit of a jumble. ENFJs, ENTPs, ISFJs, ENTJs and INTJs, all use it, though not as intently as the FPs.
Strangely, INFJs are missing from that list. This might just be an artifact of the limited sample size, but it's possible that it isn't a priority. Instead, it appears that INFJs rely on literal details (exact words used) and a strong social context to evaluate people. Combined with their Ni, it amounts to being a very similar thing, but it's remarkable to see how the evaluation might be different.
On a side note, I recall that there was a "Sense Motive" skill in D&D 3rd edition, which is kind of analogous to what Elfboy is claiming in the OP. One thing that I kind of wanted to add to that system (I no longer play), was a "Deduction" skill that was more Intelligence-based, which would work sort of like Sense Motive, except it would be about spotting inconsistencies in a more thinking-style, than feeling style. I bring this up because it is entirely possible to have a thinking-based bs-detector, except it isn't detecting duplicity so much as it is likely detecting incompetence or ignorance.