Check the DC lemma, does it say that the map in model cat is unique or unique up to homotopy? Cisinski email says up to homotopy (“a unique map HB–>D in the homotopy category of (commutative) ring spectra in the strongest sense possible (that, a map of commutative monoids in the model category of commutative ring spectrum, which is unique up to homotopy in the model category of ring spectra)”). So the new insights of Jakob/Cisinski might be much needed after all.
nLab page on Canonical hofib?