The idea that any form of price optimization among firms violates antitrust laws would put basically all management and marketing consulting at antitrust risk. This doesn’t sound plausible.
I don't know if what Patrick does is problematic. It wouldn't surprise me if he was trying to be glib and his actual advice is more nuanced.
If one interprets it literally: Someone who receives advice from him to raise prices can look down Stripe's customer list and find its competition and feel confident that the competition will receive the same advice.
Again, I don't know what he does. All I know is that what he says if read by the right person would be sufficient to trigger their curiosity to ask for records of his correspondence and find out.