Valve then forwarded us the statement from Nintendo's lawyers, and told us that we had to come to an agreement with Nintendo in order to release on Steam.
We all know Nintendo is a bitch and there's nothing illegal in emulators, but Valve's stance looks reasonable to me, it would be serious damage to Steam if they were involved in legal litigation.
Correct. Valve could have let them release it and let Nintendo go through the DMCA process. As long as Valve follows the process, they would not be the subject of any litigation.
In terms of user content this would be correct. However when it comes to games on the platform valve does do curation to ensure games run etc. I don't know if it has been tested, but that curation could exclude them from the protection. If that was the case they could be directly sued for copyright infringement.