Well, I wouldn’t use such strong words as “lying” or “should completely redesign how their tools are working”. Technically, they have not much chances to work correct in a scenario with a transparent proxy (like Avast web/mail shield) unless they would somehow “hijack” the proxy (which would have to be done uniq for every single transparent proxy).

Another story is, that the “process based” approach does not work very well even without Avast installed on modern OS X versions as various processes are accessing the network using a single “webkit process”.