I agree that he is right to point out the problem, and to avoid singing it himself. I'm not sure if he's entitled to make a blanket rule for his congregation. Are we sure that it was his own action and not something that he suggested?
In my experience, the media likes to portray clergy - Anglican or catholic - as autocrats, even when the decision has been taken by a parish council
I've always taken it as poetic licence, and part of the general mawkishness of carols - like "No crying he makes" - it wouldn't have been all that still with all those cessor candidates milling about and all the inns full!