The Constitution determines the Law.
The Law does not determine the Constitution.
The Constitution only says "natural-born." It is up to the Congress to determine what that constitutes natural-born within any reasonable interpretation of the phrase, and we have the courts (supposedly) to keep Congress from going too astray in its determination. Given that this was the first Congress, which was full of our revolutionaries and which wrote the Bill of Rights, I tend to believe the interpretation of 1970 was what was meant.