I was thinking that the King issued the invitation which left it up to Andrew whether to accept or decline. It would head off the media stories about Andrew being "brutally snubbed" by his brother while on holiday at Balmoral. I believe the "snubbed" stories popped up at Easter and at Christmas also.
Since I'm not friends with the King and Queen, it could have been a sincere gesture or a gesture to keep Andrew from complaining later that he was left out of the family gathering at Balmoral.