Or in the case of a citizen of said country it’s, “you want to return home, play by our border rules, and btw you have no citizen rights because the border isn’t the country.”

Can a border agent refuse entry to a citizen of a country?

They can in some countries. China for example.

America has de facto exile due to the No Fly List:

https://www.theguardian.com/commentisfree/cifamerica/2010/ju... https://www.aljazeera.com/indepth/opinion/2013/02/2013241659...

https://www.thedailybeast.com/one-womans-case-proves-its-bas... https://www.courthousenews.com/en-banc-9th-circuit-takes-up-... https://foreignpolicy.com/2018/05/01/who-can-challenge-the-n...

Snowden is arguably in exile, as his passport was cancelled, but he wouldn't be refused entry :-)

> It's more along the lines of: you want to visit, you play by our rules.

PoTAYto, poTAHto