Archie isn’t on his own, he’s with his nanny who probably looks after him most of the time anyway.
Nobody means literally on his own. They mean no one who is family or friend.
A nanny is not a replacement for Mummy and Daddy. I certainly wouldn't want my child developing a closer maternal bond with my nanny unless I had no choice. Very Victorian and bad in terms of attachment as the Nanny eventually gets her P45 and has to move on.
But as OverUnderSidewaysDown says maybe he's here.