If the 20% figure you gave was accurate for a particular site, then your conclusion would be absolutely correct. That particular site shouldn't have done a fixed-width 960px layout.

However, as someone who was a webmaster in 2007, I can tell you that the 20% figure was not even close to true for my particular sites. Other webmasters I knew told me the same.

So I'd say that this, like all things in web design, admits of no hard-and-fast rule. Rather, the answer is "it depends." In 2007, it depended on what your analytics were telling you. Most sites nowadays have a strong business need to support phone-size displays, but even today, not every single site does.