Err no you didn't get it.
Actually it does use non long tail distribution see the whole 95% figure etc. Those are assumptions about the distributions.
Edit: it does make one assumption, namely that there will be a finite number of humans ever.
> "Because it can be applied to completely arbitrary distributions provided they have a known finite mean and variance, the inequality generally gives a poor bound compared to what might be deduced if more aspects are known about the distribution involved."
In the situations cited in the article, we are dealing with both an unknown mean and an unknown variance and therefore an unknowable distribution. So while Chebyshev is "weaker" than a Gaussian distribution, it's still a distribution.