Turns out the biggest decay factor is nanograting and the biggest contributing physical quantity is temperature. They plotted what decay would look like on an Arrhenius plot. They both computed estimates and measured to confirm: the measurements are quite accurate. The specific claim is that they computed that it would last 13.8Gy at a some reasonably high temperature (462K). They could've picked any other point on the time/temp scale, like "here's how long it would last at room temperature" or "here's how hot you could store it if you only cared about it for a billion years".
They did not, however, simply make up a number with no justification, let alone commit straight-up academic fraud, as you're implying.
The paper is here: https://www.researchgate.net/publication/297892219_Eternal_5....