Clearly, the Westminster Assembly either a) used their own authority or b) appealed to some other authority to determine that the deuterocanonical books are not "of divine inspiration". That Maccabees, Tobit, and other "apocryphal" books are so named, rests squarely on the shoulders of some authority under which the Assembly operated.
So who is this authority? Their answer comes in the next two points.
4. The authority of the Holy Scripture, for which it ought to be believed, and obeyed, depends not upon the testimony of any man, or Church; but wholly upon God (who is truth itself) the author thereof: and therefore it is to be received, because it is the Word of God.
5. ...our full persuasion and assurance of the infallible truth and divine authority thereof, is from the inward work of the Holy Spirit bearing witness by and with the Word in our hearts.
In honor of my friend, Rachel Held Evans, I call this "playing the God Card" in the game of scriptural interpretation. I agree that God alone can interpret Scripture; the problem lies with the last three words of point #5, "in our hearts". The traditional understanding before the Protestant Reformation was that God revealed the truth of the Scriptures through His Church - that is, through those leaders who were spiritually descended from the Apostles. Now, everyday Christians have just as much a right to make interpretive claims as the most educated Biblical scholars.
So what happens when anyone can interpret scripture for him or herself? You get an explosion of denominations like we now see in the Protestant world. Baptists, Presbyterians, Methodists, Pentecostals, Bible Churches, Church of God, Church of Christ, Lutheran, Anglican, and many many more. Most, if not all, of these denominations now have daughter groups of their own which have splintered off over typically minor - though sometimes major, admittedly - doctrinal issues.
And every single one of these groups claims to be following the Holy Spirit's interpretation of Scripture. I am amazed that the Holy Spirit would say so many different things to different faith communities.