Well, I didnt think I was disagreeing with you in any material respect, but it depends on how you define accuracy. It is possible to measure a speaker's frequency response, and get a flat reponse, but still have high levels of distortion. Of course, you can include low distortion in your definiton of of accuracy, but I think it best to keep the concepts distinct.
Take a look at the measurements of the Mirage MRM-1 at soundstage.com, equipment archives, loudspeakers,and scroll down, or just try this url
http://www.soundstagemagazine.com/measurements/mirage_mrm1/
Not real flat, but not a bad frequency response, yet, to me, unacceptable levels of noise and distortion in the bass (where almost all speakers have a problem) and midrange. No real correlation with the FR, they are separate measurements.
I know from personal experience that when I play a 50hz tone through my Harbeths, I hear a 50 hz tone coming out of them. No audible distortion. But when I play the same tone through a pair of AE Aegis Ones, a pretty good little $300/pair speaker, though the spl meter reads about the same, I hear something that sounds more like 58-60 hz because the output includes the fundamental plus some doubling and other distortion components.
The reason I say low distortion is more important is that we adjust to different tonal balances in different venues all the time, so moderate FR inaccuracies are not always troubling (some are), but distortion is always annoying. A frequency response inaccuracy means the notes are played a little too loud or a little too soft (if in the fundamentals part of the midrange). You may not notice, or may not care. But distortion means the wrong note.