Yes he does. With the very next sentence. Surprised you missed it because it was IN THE VERY NEXT SENTENCE.
Madison said:
"Mr. Smith founds his claim upon his birthright; his ancestors were among the first settlers of that colony."
So when he says "it will therefore be unnecessary to investigate any other", and then he immediately investigates Mr. Smith's "birthright" and "ancestry", I do regard that as a contradiction of his own statement. If place is all that matters, why mention his family? Your argument is done with "he was born here." End. Period. Finito. Full Stop.
No he doesn't. Having defined natural-born citizen as one born in the country he does not contradict it anywhere. You build in a definition of 'birthright' that Madison obviously didn't use.