You didn't read the QAI Listing, did you? The QAI Listing is for Fire Retardant COATING. The I-Codes recognize fire retardant COATINGS for non-structural applications, such as interior finish.
For structural, refer to IBC Section 2303.2. FRTW must be 'pressure impregnated'[paraphrased for your benefit]. As a result, FRTW is allowed in lieu of non-combustible materials in certain applications. The legacy of this approval goes back to full scale white house testing done decades ago. FYI: Even UNTREATED wood large timber actually outperformed steel in some other testing that was done in that same timeframe. Some very interesting pictures exist from that testing.
IRC (residential/townhouses) allows FRTW in one application in lieu of non-combustible, that being 4 feet either side of the party wall (roof sheathing). Coatings are not recognized in the I-Code/IRC either.
So, the QAI Listing is actually worthless, even if you don't consider it is for Doug Fir LUMBER only. You picked up on that, too, right? But to be fair, I wouldn't be surprised if QAI penciled in plywood at some point. When you can't get a Listing at UL, you go to QAI.
The library may have a copy of the I-Codes you can refer to, you can buy a copy, or maybe somebody has posted the copyrighted material on the web. I know you won't believe anything I have posted, but maybe you'll believe the ICC.
For those winding down for the day, you can watch the code hearings live on the web right now (though they are on a break at the moment). Go to the ICC website and search around for the link. One of my many sources for information on building material requirements.
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