A PING for your thoughts on post 28 since it ties into the discussion yesterday.
My theory is that they put the phrase in the 1790 act out of habit from using the term, but the then extant philosophers of natural law pointed out to them that Congress had no power over what is "natural", and in the subsequent revision of 1795, they corrected this oversight.
Possibly people also pointed out that it would be interpreted as granting foreign born children the ability to become President, and perhaps the congress, on second thought, didn't want to go that far.