No, I wouldn't. As stated in post #13, there's a noticeable difference in frequency response between the amp models in the II and III. Single coils can sound a bit shrill through some of the Fender models in the III, while likewise sounding normal (ie. not shrill) using the same guitar, at the same settings, through the same models in the II.
No one's suggesting the III is responsible for the OP's fret buzz. What's being suggested is that the frequency response of the amp models in the III may potentially be a contributing factor in accentuating it, and serve to explain why the OP feels it's more pronounced in the III vs. otherwise. However, as mentioned in post #9, I'd like to hear a sample.