Obviously, analyzing consumer prices is a pretty subjective task because every single person's utility is not exactly the same for every single object (the added benefit of that dollar would never induce you to scrimp on your pepper choices). I think that's why the second part of Williams's argument makes sense—that because the test is subjective, you can mess with it—although in this case there's no evidence to substantiate foul play.
No matter how you slice it, however, so long as the BLS keeps a pretty standard list of which goods can be swapped for which other goods, the use of its data as an index nonetheless holds up. Yes, not every single person is going to make exactly the same decisions, but their data-driven "average person" always will. So as long as the economists at BLS don't regularly fiddle with their criteria (and there's really not much evidence to support this assertion) then their way of measuring CPI works as an indicator.
(Also, food is not evaluated with hedonics.)