The point is that the recipient of the money doesn't interact at all to receive it; the rest of the network just "decides" (based on the transaction) that such address now has X more coins. The machine with the address/wallet is not consulted.
That is not the point. The information could be available, and the recipient could therefore act on it. If the information is not available then that is the point - but that could in principle be the case even if there was interaction.
