Without pointing any fingers (... tempting...) I would be surprised if the head coach is responsible for checking players' eligibility. It's not his main task to focus on.
He may say "I want this guy", and he will be told by the team management "No you can't, because he is not eligible, but thanks for asking - we'll send off an application to FIFA just in case, now that you mention him".
More than one person should have looked at these things, in a well-run organisation. With so much at stake, an apology is not enough - it needs a very good sweep with an HR broom. With this bunch, I won't hold my breath though.