the most famous case I can think of was St John Chrysostom in Pittsburgh and the argument that those who built it didn't see Union with Rome as foundational. They ripped up the carpet to reveal the Papal Coat of Arms done in marble in the nave. The parish remained Greek Catholic.It doesn't mean that most parishioners who founded the parish saw union with Romann Union as foundational to their group.
Yeah, it was just the parishioners who sponsored the Papal Coat of Arms done in marble under the carpeting. Maybe it was like two really rich people with a Western fetish.
Or maybe their perception when making the parish was like that of some Maronites or Melkites who claim (incorrectly I suppose) that they don't have to accept all Rome's theology.
Now and then the RCs talk about doing a reunion with us Orthodox, and they claim somehow that Papal Supremacy need not be a total dealbreaker. If some Orthodox bought into that claim and signed up with the Pope, a somewhat similar situation could result, where the Orthodox imagine that they are on somehow equal terms with the Pope (eg. first among equals or something), or that Rome is not foundational to them in their union.
The people who made the church building could imagine that Eastern Christianity and their group of Eastern Christians was more important and thus foundational to them than being under the Pope. So when their Eastern Christian group decided to go back to the Orthodox organization, they would see it as still being Eastern Christian and thus staying within their main foundation of Eastern Christianity.