There is a legitimate argument to say "perhaps some of them thought it flowed from English common law, while others believed it to be derived from Vattel."
There is a possibility this is correct, and this may partially explain some of the confusion.
However, many of them wrote what they thought on the matter, and so we can discern from their writings what they believed to be the meaning of natural born citizen.
But just because I don't agree with you, doesn't mean they are against me. There is plenty of evidence that they agree with me, especially men like Benjamin Franklin, John Marshall, and James Wilson.
The definition of what NBC meant to the Founders was explored in depth and with accuracy in Wong Kim Ark.
https://www.law.cornell.edu/supremecourt/text/169/649
Birthers don’t like it because they prefer the bad translation of Vattel...but one should interpret the Constitution based on what was put into it, not based on misconstructions hundreds of years later in an attempt to throw Obama out.