Yeah, I don't think it was even that, just saying he knows the company involved in the same way he often says he worked with some production company when they come up as involved with something on the podcast.
(I mean, I agree with pps that he's getting awfully blokesplainy of late, and keeps interrupting MH, but I don't find it problematic that he said they were his publisher. I think it was relevant in the same way that MH saying she was currently adapting something for the screen was relevant to their point about how small the reading public is compared to the people who will see a film, or at least be aware of it via actors doing promotion etc).
One of the other things that struck me in the TRIE episode was that they placed The Salt Path controversy squarely in the context of the current fixation on 'authenticity', and the appetite on somewhere little Tattle Life for analysing influencers for inauthenticity/white lies/ omissions in the way they present themselves, which is seen as a betrayal.