This sounds like anyone can make the claim. If they set foot in the office, they have a claim. Perhaps someone substituted for the usual janitor one night; then he shows up with a claim. Maybe someone had lunch in the same restaurant nearby, chimed in with a sarcastic comment about anything, and shows up over two years later with a claim.
I cannot fathom the situation being tenable.
"It would have been easy to have something be written up and signed for next to nothing right as Jeremy left." And if Jeremy refused to sign? Would that have been further evidence (e.g. of Kyle trying to push Jeremy out) Jeremy can use against Kyle in this situation to say he's owed more?