> I suspect it's just bad design.

I don't have good suggestions on what would improve the design while staying with the general approach, but I imagine reporting a "likely not significant" could have at least be improved to a "proven to be not significant" null result by adding the "obvious" control group. Just check how "unlikely" mentions of common memes and catchphrases compare to those brands. Are there non-brand mentions that are distributed similar to the brand mentions, showcasing that these numbers really do not mean much either way?