Right now at least, if empirical testing shows poor results and anecdotal usage shows great ones, I'd say that in fact anecdotal evidence holds much more weight. The empirical testing is just bad.

So you make it demonstrate the ground facts. Show formal proofs, link to and reference specific documents and fragments in a document database. It wouldn't really be that hard to build a harness with specific support for these things (e.g. performing a tool call that then has UX to highlight fact-checked claims and link to details/references).