Citizenship indeed is a relevant factor in terms of what happens when trying to leave to the country of citizenship and encountering "stay at home" regulations enforcement in the country of residence for the foreign citizen. That said, how it plays out is a situation of YMMV in places when heading to the foreign country of citizenship. If this was a situation where the US citizen is a known UK citizen whose ties with the UK are obvious on their face and US residential ties seem non-existent -- think of someone like Boris Johnson before he formally renounced his US citizenship -- then it could be a different story.