You're asking questions that can only be answered in context, without context.And people perform a song and dance instead of simply saying ‘yes’ or ‘no’
So let’s go back, the players ask in Buckingham Palace for an audience with the king. After doing so (and before getting an answer) one points out ‘we are in a different world, no one knows us, they won’t recognize our nobility and think we are just some crazy people’. The players discuss this idea and decide that yes, this is in fact a much more reasonable expectation.
So, given how the rule is written (no exceptions, they will be recognized), do they get their audience or not? In other words are they able to violate game rules while at the same time insisting that under no circumstances whatsoever the DM could.
What you're asking is can the players and GM, by consensus, suspend the rule for the Noble background? My answer is, it depends on a whole lot of other considerations and expectations particular to that table.
For instance, suppose that in a previous session the Position of Privilege feature had mean that the Noble PC had had trouble passing incognito, disguised as a day labourer. (In Burning Wheel, the Mark of Privilege trait - which all born noble PCs have, at least to start with - imposes +1 obstacle to Falsehood and Inconspicuous test when pretending to be of lower station.) Would it be a type of "cheating" for everyone to now conveniently ignore that past episode?
I would not expect every table to go the same way on this.