I was not informed about their thumbs down by Airbnb, you're exactly right in that my discovery was by inference.
I got the booking request for a week long stay and accepted immediately because I love it when that happens. Then I got a little nervous because I realized that we were on instant-book, and we should not have gotten the request, they should have just booked, right?
I then took time to look at all the places they'd stayed, the reviews they left leading me to the reviews they received. I saw that their last host left a pretty bad review (broke house rules, big mess to clean up which required outside help). I immediately contacted the previous host (sending them an inquiry) to ask about what happened. She was not at all encouraging. She said that in her 20 years of renting she had never seen such a horrible mess. Thumbs-down.
I did see though, that the previous host's style was very "old-school French Gite", i.e. check-in and out only at noon on Saturdays, completely unequipped rooms (previous guests remarked on lack of cleaning supplies, no toilet paper, no coffee), rules upon rules. These rentals are a tradition here in France, usually rock bottom cheap made for budget-minded French families.
Then the people came. Very nice people, but I was also nervous. I invited them down for a glass of wine their 2nd day and at that time I asked about their last stay, was there some problem? They said no, not at all. They did see that the host had asked for more money for cleanup which they paid, because they were not aware that the cleaning fee didn't cover clean-up. They implied they'd left some dishes. I replied that in my experience, the "cleanup" for a host usually entails laundering and changing the bedding, fingerprints and dust, replenishing supplies, and cleaning the bathroom. They pondered on that a bit I suppose because when they left, our place was spotless. All's well that ends well.