I can't think of any type that can't "fake". Actually a funny thing... IXTps often act more like Fe types than IXTjs.
It also depends on what we mean by "fake". If by fake we mean "lying", then lying is not related to any functions. If by fake we mean more emotional or relational fakeness, then Fe or Fi types have a much easier time, just because they have access to so much information and they know exactly what they're doing, and how. But just because it's easier for them doesn't mean that they do it, and just because they're bad at it doesn't stop them from trying.
And then we may even stop understanding what "fake" even means... how do we define fake. I think all we can say is that there are general trends of such things, but they're not absolute.