yes but practically big businesses can get away with these types of things without much fuss. even in the case where Apple and Google were caught wage-fixing, and there were emails from the CEOs blatantly colluding to prove it, all they got was a slap on the wrist. So it's effectively legal in my view
Neither publication not open admission are necessary for a combination in restraint of trade to be illegal, and you'd usually want to avoid them since they make it much easier to prove.