"All heretics quote Scripture. The question in this controversy is not the normativity of the Bible but who gets to interpret it."
He is quite right; that is the question. What he means by "who gets to interpret it" is: Whose interpretation is authoritative?
His reason for thinking that the interpretation [made by the denominations] that he cites is authoritative is that those denominations agree with his own interpretation. But then, that is no different from FV advocates starting their own denomination and appealing to its interpretative authority. So Clark is treading on very thin ice, ice so thin that he has to leave the problem as a question. If he goes any deeper, he will expose the fact that the ecclesial authorities to which he appeals are merely "doctrinally grounded authorities", and not "sacramentally grounded authorities" (see here). There is no principled difference between the ecclesial authority to which he appeals, and the ecclesial authority of a denomination his interlocutors could set up overnight. That is because anyone can set up a doctrinally-grounded authority. Just put out a shingle.
Apart from sacramentally-grounded authority one person's interpretation is no more authoritative than anyone else's. Apart from sacramentally-grounded authority, the answer to the question: "Whose interpretation is authoritative?" is "Everyone's", which is equivalent to "No one's." Those who reject sacramentally-grounded authority should never appeal to magisterial authority to oppose a position, because those holding the opposing position can simply install an alternate magisterial authority, and then the two sides are 'even'. It is better to call non-sacramentally-grounded ecclesial authority for what it actually is: individualism, and not pretend to have a magisterium. In short, it is better for someone in Clark's position [who rejects sacramentally-grounded authority] not to say what he says in the quotation above, for what he says in the quotation above is the theological equivalent of cutting off the branch on which he himself sits.