When I saw this I thought the authors badly mangled Chebychev's inequality. So I checked out the paper you're talking about because I thought there might be more context to the quotes that would explain this... but there wasn't...

However I think they used Chebyshev's inequality correctly but just did a piss poor job writing what they meant. Chebyshev's inequality tells us that 93.75% of the data will fall within4standard deviations of the mean (not the 8 like is in the paper) and 96% will fall within5standard deviations of the mean (not the 10 like in the paper). Notice that they incorrectly doubled the number. I think they meant to say that 93.75% of the observations fall within 4 standard deviations of the mean - which implies that over a range of 8 standard deviations we observe 93.75% of the data. Over a range of 10 standard deviations we observe 96% of the data. So if we treat these values as essentially containing the entire range of the data then without knowing which standard deviation we're talking about we might expect that between 1/8 and 1/10 of the observations fall within that specific standard deviation. This gets us sort of close to what they wrote because this gets us 10-12.5% (not the 10-15% reported in the paper)