Actually, I think how your director has phrased it sounds right. Due to his hectic schedule, he would be better suited for the understudy, that way he does not have to worry about missing out on work, and the show can go on.
If it helps, you can say, "Due to your hectic schedule, the Director feels it's best for you and the show, if you were to understudy the role of X. We still want you to be part of the production, but we understand that your schedule won't allow you to attend all of the rehearsals necessary for the performance."