It seems like I was operating under a false understanding of it, and I'll remember that for the future.
> Japan actually has much narrower restrictions on who can become head of state than the US does. It just doesn't combine that role with the head of government.
Sure, fine, you can only be the Emperor of Japan by blood, just like you can only be "The Queen" (as recognized by the UK, Canada, and Australia) by blood. It's a ceremonial role, and I don't think it impacts my overall point.
This is why it became a thing with Obama. If he was born in the US then it was unambiguous. If he was born outside the US then the aggregate circumstances of his birth had a legitimate potential, under the rules at the time, to deem him not “natural-born”. It isn’t terribly surprising that people with a political angle were going to litigate that in the court of public opinion, and the vast majority of Americans have no idea how those citizenship laws work.
No the consensus is pretty clear and only gets muddied up when there are political reasons for trying to invalidate someone's presidential candidacy. To become a citizen involves going through a "naturalization" process. A natural-born citizen is anyone whose citizenship came by birth rather than through naturalization. There may have been some ambiguity when the Republic was young, borders were porous, and documentation to track births and deaths and such was scarce or easily forged. But today we've got that all pretty much locked down.
True, though there is no clear consensus on what the former means, it is clear it is narrower than the latter.
> The law in America forbids a foreign-born citizen from being president.
That is not one of the major theories as to the import of the “natural born citizen” rule.
> By contrast, according to the wikipedia page on the subject (https://en.wikipedia.org/wiki/Foreign-born_Japanese), Japan has no restrictions on foreign-born citizens.
Japan actually has much narrower restrictions on who can become head of state than the US does. It just doesn't combine that role with the head of government.