Really which Presidents weren’t natural born? You can exclude the founding fathers and anyone who was a citizen of the US at the time of the signing of the Constitution. They are eligible via the Constitution. Please name two.
So the courts may some day sort it out. With widespread travel and foreign assignments so prevalent, I'd be shocked if any court didn't take a fairly broad approach. To do otherwise, they'd have to go back to "original intent," which was to keep British loyalists from bringing their progeny, setting a stooge in the White House and re-taking America (as they almost did in the War of 1812).