One extra data point for you. Not long after I posted that last message, I started getting the same error even with the whitelist disabled. I disabled the entire plugin and still got the error, which is when I started wondering whether it might be simply WP SuperCache serving up bad old static data. I purged WP SuperCache's cache too (don't want to be served up old pages with that error), and then re-enabled AVH First Defense.
At this point I don't know if it was truly AVH causing the issue or another sort of caching error involving WP SuperCache, but right now AVH is enabled (with APIs + local white/blacklists enabled, too) and WP SuperCache is active too. And the error is gone.