yes, ultimately the DM decides. In no way does this mean he can just abuse that position and force the players to do whatever he wants, but it does mean that he can deny an action the player would like to take when from the DM’s perspective there is a good reason why it should not be possible.
When push comes to shove, one person has to decide, for me that will always be the DM. 99% of the time we are not in that situation however and things get resolved cooperatively.
The premise was ‘because the feature says the noble can get an audience, that means there is no way the DM can ever deny one’, I disagree with that, pure and simple.