Are you suggesting US law requires companies to aggressively try and poach each others staff? That would be remarkable and amazing if so. What if you aren't particularly interested in staffing a large recruiting division, and don't cold-call anyone? What if you think cold-calling is like spam and just feel it's not something your company should do? Do you get in trouble for holding down wages?
No, he is suggesting that making a mutual agreement not to do so is illegal, just like a whole range of other actions that have price setting effects are legal when a company does it in isolation but illegal when multiple companies collude to affect the pricing.