[NoboruWataya]

Exactly. Both sides will have copies of all pertinent evidence, and if their copies conflict in any material way, it will be noticed and investigated and the party that manipulated their copy is going to have a very bad time.

The examples given in the article rely on an attacker manipulating an image prior to it being hashed, or compromising their opponent's database. If you can (and are willing to) do these things, no hashing algorithm will help. They also assume that the hash is literally the only thing anyone will rely on in identifying a document, which is not how it will work in practice. (No witness has ever said "yes there was a letter, I don't remember what it looked like or what it said but I remember its MD5 hash was [...]".)