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The supplementals-only query above gives me urls that also show in the regular search results without a supplemental tag. They even have the same cache date in both incarnations. In fact, some other site: operator queries also show the same url/cache date without the supplemental tag.
So what action can I sanely take on this basis? My concern is that these queries are tricking the site: operator into a worse-than-usual level of accuracy by asking them to perform outside the way they were designed.