You've defined it as "no restriction whatsoever on who can physically enter the country."
So if the restriction is that you must actually have a passport, would that be enough?
I guess I am still not sure what you mean by "no restriction whatsoever on who can physically enter". I don't seem to have any restrictions to physically entering Ireland - I just have to show a passport and answer some questions.
If migrants were let to come in and do as they please simply by showing a passport and answering questions, would that then be a non-open border?
Is someone proposing we no longer require anything (any ID, answers to questions, etc)? "I'd like to get across this bridge". "Who are you and why do you want to come the United States?" "None of your business". "Thank you, and welcome to the US".