its how most people identify now. back in the early 1800s it would have been more correct to say "state" vs "country". back before the romans in europe it would have been more correct to say what "people/race" you belonged to rather than "state or city". back before civilization it would have been more correct to say "tribe/clan" than "people". maybe at some point in the future "nation" will lose its meaning but it hasn't to date.
there is nothing tying a person not born to here. at least with birth, and up until adulthood, you don't really have the ability to self determination. so its not like one is making a conscious decision on where they are at that point. and when you don't have that choice, "nature" would default that existence to a right of existence in X. imo.
once you are responsible for yourself and make a conscious decision you have taken responsibility for your own action, which removes the blanket fall back of a "right to be in X, because you have nowhere else to be". because you are choosing to be in "X", rather than it being a default, no other option.
which is why I am generally for asylum in this country. I don't like the way its been used currently, but I do think its an important thing we should honor, and have been against many of Trump's removal of asylum status for some peoples. my "ideal" there, would be if Mexico or Canada, or Cuba, and the Bahamas and Bermuda for some reason made it so a native couldn't live there, I have no problem with those people having a "right" to asylum here. because we are the next door neighbors. there is no other option, so there is a default back to a "right" of asylum. but once you have to pass one place, to get here, the asylum seeker is making a conscious decision of where they are going rather than just being pushed into the next spot. so that second person seeking the same "asylum" would not have a right to be here and would be at the leisure of our government. which is why I also push back on you labeling my argument as "if you can't legally exist here its the same as saying you can't legally exist anywhere". there is a always a limit and its up to the natives to set that limit.