Congress “amending the law” is the very antithesis of “natural.”
Congress clearly cannot amend the Constitution (although it can propose amendments to it).
Congress clearly can amend statutory law.
In context, you think it was clear upon the adoption of the Constitution what natural born citizen meant and that the Congress can’t change that original intent. There is precedent for this. It’s the Dred Scot case.
The Supreme Court ruled 6-to-3 that “all men” in the Declaration of Independence meant all White Anglo Saxon Protestant adult males. Hence, Dred Scot could never be a citizen of the United States and, so, had no standing to assert his freedom.
Abraham Lincoln, in his Cooper Union speech laid out the alternative position, that it meant what it means in Standard English, and cited numerous evidences to including Supreme Court precedents to that effect.
Take a look at the body of the Constitution, at the power of Congress regarding naturalization. Notice that Congress had the power to establish a “uniform” law regarding naturalization. If you would think about this, it implies that each state defined who were its natural born citizens and how somebody not a natural born citizen became naturalized.
Of course, each state deciding natural born and naturalization for itself had to be the case prior to the U.S. Constitution, from 1776 to 1789.
Now, let move forward. How was citizenship handled in the Northwest Territories? Did the Continental Congress provide for it, and did the U.S. Congress?
When we acquired the Louisiana Territory, how was citizenship handled? Could it have been that the Congress did it, or that the Senate did it (in the Treaty)?
When we annexed Texas, and then when we acquired the territories we got from Mexico after the Mexican-American War, how was citizenship in these places handled? By act of Congress or by Senate-approved Treaty?
When you think about these things, I think you’ll accept that the Constitution sort of failed to address the specifics of what “natural born” means. I say “fail,” because the Constitution doesn’t give Congress the power to decide who is a natural born citizen, and yet contingencies such as acquiring new territories would seem to require the Congress to recognize citizenship.
Most students of the Constitution agree that it’s kind of nebulous about natural born and that the Congress has asserted itself where there is a void. It is, therefore, understandable for people to argue the matter. The thing pops up from time to time. Members of the other party, and nativists regardless of party, can be counted on bringing the issue whenever a candidate for President falls short of the strictest possible interpretation of natural born.