That's a historical argument, not an exegetical one. And even if it were true, it doesn't change the fact that they had to arrive at that position "by good and necessary consequence" since there is no specific command to sing the "Book of Psalms only".
Even the Confession does not say "Book of Psalms only", is just says "singing of psalms" (21.5.), which is the only reference to song in the whole standards. Yes, many (not all) divines held EP, but even they did not enshrine the "only" when they had the opportunity. It's a little difficult to call it an "EP document" in light of a single reference. All others since then have had to supplement the Confession with an EP or non-EP interpretation. For example, the RPCNA had to supplement the Confession with their additional Testimony to affirm EP. Later denominations like the OPC and PCA do not interpret "psalms" as "Book of Psalms" but a more generic meaning of "songs", without any change in substance of the regulative principle articulated there, just a different interpretation about what is actually commanded. The need for later supplements show it was not an obvious "EP" document at face value.
But ultimately, it matters more what Scripture commands than what the the Confession says. A more generic understanding of "psalms" does not require amending the Standards, only properly understanding what the proof-texts actually say. Developments in doctrine and terminology still occurred after the Confession was written, which we also consider to be standard terms for orthodoxy now even though the Confession did not say them then; for example the imputation of Christ's "active obedience", the "covenant of redemption", and even more recently the "regulative principle of worship", etc.
I don't want to derail the thread by an argument about the Confession's original intent or the animus imponentis of later denominations, so if anyone wants to discuss that further, it's probably wiser to start a new thread. I just wanted to point out, even the Confession is not as clear as my brother, Randy, would like
And the exegetical argument is the one that matters most anyway.
Two cents...