That X-Files episode may have been inspired by "Time Shards" [1] by Gregory Benford, a short story first published in 1979.
TLDR: Too late to be included in the bi-millenium vault, a Smithsonian researcher discovers an audio recording accidentally inscribed on a c. 1280 pot by a pointy tool cutting a decorative spiral. After listening to the banal conversation recorded on the pot, the researcher wonders about the contents of the vault to be opened in a thousand years: “What makes you think we’ve done any better?”