All contracts are negotiable, you did nothing wrong other than not having a conversation before wasting paper, the main issue is that for most people the negotiation is "if you want to work here you have to agree to all this."

But yeah reasonable accommodation and mutual understandings, etc, should be written down and signed. I challenged the non-disclosure agreement at my job once because it literally said I couldn't talk about my work with ANYONE, and a plain reading of it would mean I'd be unable to even talk to my boss about what I was supposed to be doing. It was poorly written and probably unenforceable. My boss didn't like that so I signed it anyway and then focused on finding work elsewhere (he was a dick and his company got raided by the FBI a few years later)

Did you sign the fresh copy?