When I had a look at it earlier I deliberately tried searches that probably wouldn't bring up "top 5,000" sites, to see whether that warning applied universally. By "reasonably irrelevant" I just meant things like - actual examples - "garden furniture" and "dairy products", which had no direct bearing on my own interests or any specific sectors or themes I see here.
I also picked things that I thought were unlikely to have "top 5,000" sites in the results to confirm that the "warning" applies to most mundane product, service and information sites. As far as I can see, it applies universally, even to PPC advertisers.
However, on thinking about it further I thought I should try something that would be more likely to bring up "top 5,000" results. Initially I tried "world news", in which (obviously geolocation-biased) the top result was BBC world news. This didn't have the "Site not in top 5k sites" warning, so is clearly one of the top 5,000 sites in whatever metric(s) Google uses. However, it still got an amber flag and a score of 1 ("Haven't visited site in the last 3 months") so my earlier assumption was correct.
I navigated away, then back again to see if the "haven't visited..." warning had cleared, but it hadn't. Closing and reopening Chrome didn't clear it either (it is still there after a couple of hours), which is in itself interesting. Possibly my personal security and privacy preferences in Chrome are being respected (all credit to Google if they are), leaving Google without any information to tie my browser identity to the previous visit. Possibly, however, there is some time-lag or other factor involved.
It is certainly interesting, but I really don't see where they are heading with it. I can't think they will get enough reliable and unbiased human input to hang a coat on, let alone a worldwide "trust" policy. Iamlost's question is interesting too: apart from the 3 months warning (or other changes in status, like entering the top 5,000), will any site ever be "unmarked", and what about going in the other direction: is there a "red-flag" marker that will come up saying "multiple reports of suspicion"?