Goodwin and Owen certainly consider various readings, when there are any, and then make judgements based on that. I don't think Manton is any other, but his judgment in this particular case is simply that a few testimonies don't deserve to put away the general consent of the church, as he calls it there.
I don't really understand what the guy on Facebook is trying to say. Certainly not that Manton or the puritans were King James Onlyists or something like that? Because I am pretty sure (even though I never studied it) that they wouldn't go such a route.
But it would indeed be interesting to see how exactly they were making their judgements, are there any resources that talk about that?