@Borek
Just because something hasn't been observed in nature doesn't mean it can't exist. We know CH5+ exists because it's been observed. CH62+ has never been observed, but theory predicts it is kinetically stable enough to be observed (J. Am. Chem. SOC. 1983, 105, 5258-5263). The acidity of this complex would be incredibly high and decomposition would probably occur even faster, but the point remains that in principle it should have a Ka value. Therefore both methane AND even CH5+ are, strictly speaking, amphoteric, in that they can both accept and discard a proton. (Although this isn't really a useful definition since virtually anything would qualify.) Hence the key qualifier "readily", but this is rather subjective and any definition of "readily" would be arbitrary.
Similar unconventional compounds like diprotonated water (H4O2+) [J. Am. Chem. SOC. 1986, 108, 1032-5] have been inferred from experiments as transient species. Likewise diprotonated ammonia, the molecule under discussion, has been predicted to be kinetically stable by theoretical measurements [J. Am. Chem. Soc. 1997, 119 (20), 4594–4598.], although exposure to superacids failed to produce it experimentally, so it must be very acidic indeed (not surprising). The same work DID show experimental evidence of the similar (CH3)3NCH42+, so it stands to reason pentavalent protonated nitrogen could exist if a strong enough acid could be found to prepare it. The same group even did theoretical calculations of NH63+ as well as the pentavalent version and penta- and hexa-valent versions of phosphorous, arsenic and so-forth analogues. [J. Am. Chem. Soc. 1997, 119, 12984-12985] They're all predicted to be incredibly unstable, but you never know whether some experiment will be designed to observe them experimentally. Finally, gold analogues of tetra-valent oxygen and pentavalent nitrogen have been synthesized, so those are certainly possible. [Nature 377, 503 - 504 (12 October 2002 and Nature 1990, 345, 140]. Singly-positively charged pentavalent nitrogen, NH5+, has also been experimentally observed. [Chem Phys Lett, 1988, 143, 1, 13-18.]
Point being: a lot of things haven't been observed but that doesn't mean they're not possible or that they're not "correct". Many have been computationally studied and predicted to exist under certain conditions. In the end the whole reason I brought it up is to say that "acidity" is a continuum concept. If you have a strong enough acid you should be able to protonate just about anything. How long the protonated form hangs around is a whole other issue.