Remember, the Puritan confessions were written to reform the church from Papal corruptions. I think they are very careful to avoid such.Have stood the test of time, but are by no means infallible.
As far as someone arguing with you interpretation brother, that language really scares me for the following reason:
I live in San Antonio, TX which has a very high catholic population because of the many folks coming up across the border over the generations.
I go door to door on Sunday afternoons with another brother. One of these afternoons I entered into conversation with a well educated Catholic. As usual with those holding to the Catholic heresies, his issue was one of authority. Several times he stated that he didn't really want to argue from the scriptures because it would be a matter of our conflicting interpretations. So he used the church fathers.
Brother, I don't think we can ever fall back on the different interpretations argument. The scriptures where written for us to understand by the power of the spirit, and if a brother is truly open, we should be able to dialog and reach a conclusion in most cases.
1) RCC claims their interpretation is infallible and that the tradition of the church is equal to the Bible. Nobody claims the Confessions are equal to the Word of God. The Confessions themselves say that Scripture is the Supreme Judge. Of course, we always want to go back to Scripture. I'm just saying the Confessions are a great aid in interpreting Scripture.
2) We are comparing interpretations. "You" (or whoever) has a Confession, a system of beliefs through which you interpret Scripture, whether you recognize it or not, whether on paper or not. Why do people have such confidence that their private interpretation is equally as solid as one that has been passed down through the ages in the church and has stood the test of time up to our day? All I am saying with a Confession is, "Hey, here are some Scriptures to prove my point. Here's how I interpret them, and I have a great cloud of witnesses that also interprets them this way. You should strongly consider the work they've put into their interpretations!"