See also https://xkcd.com/1494/
The idea above was about "swapping" some random document in for the standard form and presenting it to them as if it was their document. That's not good faith negotiation, that's just fraud.
I don't think it's going to hold up if you surreptitiously modify it in bad faith.
Granted, a court might still see that as fraud, IANAL.
The most honest behavior would probably be to mark additions or changes on the form they give you, if they'll fit.
Verbatim quote: "I doubt anyone would catch it".
That is not negotiating, that is fraud.
It is absolutely not your responsibility to check for the case that you give someone papers to sign and they give you back something different unless they tell you so.
It's amazing that you people are still arguing this in earnest so far down the thread. Can you think for a second what the implications of this would mean for society, if it were an acceptable form of "negotiation"? It would be even worse for the ordinary little people.
But the comment I was referring to talked about "swapping" the papers and said "I doubt anyone would catch it". That does not sound like negotiating in good faith to me.