Indeed - and so this explains why I roll my eyes at silly comments along the lines as 'they [Brits] voted for it, let them stand in a queue at the airport or lose their .eu domains'.
It would seem to be more equitable to me a least (someone who voted remain and lives in the EU) if the ballot had presented the options of "Remain" or "Remain and ignore all of the rules". But I don't think that would be particularly popular with the rest of the EU populace, and yet, effectively, it's what's happening.