It's possible it was some sort of timing thing. Perhaps my phone had somehow not been registered, or did not know it had been registered as making the purchase.
Perhaps it would have fixed itself after a day or two...
As I said, I eventually got it installed without needing to pay twice. I think the "family plan" may add an extra complication. Strangely, the "family" seems limited to 5 members which, even these days, will not handle some cases.