That's why important stuff is done in three copies -- one to each party and the third to a notary. Here the document signing service acts as such third party and it's the rare case where they have to show up and say which copy is legit.
It's also very rare -- I worked in a similar company for years and only heard of one case of disputed signing and none of disputed contents.
I would not count on a judge to read through technical mumbo-jumbo even if it's completely obvious to you how hashes work, it's probably not for them, so the company has to put a statement.
And that three-copy tradition goes back to "indenture contracts" of the 14th century, at least.
The phrase "indentured" means "cut into sharp pointy teeth" (a zig zag pattern). The contract is written out in triplicate by hand on a large sheet. Being hand-cut after the whole document is signed, it is hard to perfectly replicate that cut. Additionally, someone would write "A BIG LATIN WORD" over the area to be cut, so to forge the other piece(s) you have to recreate the demi-penstrokes plausibly.
When two copies don't match, someone is lying. The essential third copy is stored at the Notary Office, which tells you whom is lying.
"Indentured servants" were bound by such a contract.
I imagine it would be fairly hard to flawlessly forge a split document even today, at least if you used paper with long fibers and the edges were intact. Even if you match the cut perfectly, I'd bet that under a microscope you could tell that cut fibers on the two halves don't match. A remarkably solid approach considering the simplicity.
The split tally is similarly elegant.
Of course, just giving a notary a copy works almost as well.
This is exactly why RightSignature is an expensive SaaS contract and not just something you can self host for cheap: providing somebody credible to testify which document was actually signed.
It's also very rare -- I worked in a similar company for years and only heard of one case of disputed signing and none of disputed contents.
I would not count on a judge to read through technical mumbo-jumbo even if it's completely obvious to you how hashes work, it's probably not for them, so the company has to put a statement.