The "signing" usually doesn't involve any cryptography. You just express your agreement, which can be as trivial as typing your initials in a box.
It's purely a legal, not technical thing, so if you cleverly forge the document using collisions, you'll be shouting "but the SHA-1 matched!" from behind the bars.
The legal thing does make reference to the technical thing in Europe[1] (and probably elsewhere too), by making digital signatures (which use crypto) legally binding. The question is more how courts would rule in a case where a colliding document is signed. That would probably depend on whether you can prove which of the two parties authored the colliding document (since that's a requirement for this particular attack).
(Note: I don't know whether this attack is practical for qualified electronic signatures as used by EU countries.)
In UK, rental contracts are often digitally signed by the renter and landlord.
I am sure in finance world many other types of contracts are signed digitally, also under the assumption that both parties sign the same thing.