He's not talking about other nations, he's talking about the US and saying if you are not a citizen of a nation, its a foreign nation to you and they have no obligation to let you in.
> Foreign countries have no obligation to admit you within their borders.
That doesn't sound relevant.
Nobody said that they were obliged to admit you, they complained that the reasons for declining admittance were unfair. Unless you think "no obligation to admit" means carte blanche to decline for any reason, and to treat you however they like?
If so, then that is unreasonable. It is a much stronger condition than "I don't have to let you in".
Yes, "no obligation to admit" means they don't have any obligation whatsoever, and that includes doing so for any reason they see fit and not having to disclose those reasons (if any) to you.
It is exactly the same as "I don't have to let you in".
For example, I do not have an obligation to let people into my house. I can choose to let them in or decline them entry. But there are certain preconditions I cannot apply. I cannot, for example, say "you may come into my house only if you murder my neighbour". That's because I'm legally bound not to induce people to commit murder. It would obviously be disingenuous to say this means I have an "obligation to admit" them.
It's the same with immigration. They actually are legally bound in certain ways - an immigration official can't assault you for instance. It's not hard to imagine them being legally bound not to search people's phones. That doesn't mean "they have to admit people".
You're confusing yourself with irrelevant analogies. You can say, "you may come into my house only if you give me your unlocked phone," and an immigration official can't assault you because there are certain protections granted to foreigners against being randomly assaulted. It's also not hard to imagine them NOT being legally bound not to search people's phones, and if you're trying to say someone's breaking the law here then it's your burden of proof.
There’s many points you could make about the United States and immigration, but I don’t think this is one of them.