When a Bitcoin Wallet Program synchronizes its own list of Receiving Addresses, it broadcasts a query over the network, which names each Public Key / Address, and the network replies with an updated history, of whether that Address has Sent or Received any funds since the last sync, on the assumption that the same Bitcoin Wallet also stores the corresponding Private Keys. If the Wallet Program tries to Send any funds From one of its Addresses, it must Prove that it holds the Private Key, by Signing the request to do so, using Public Key Cryptography. This signature can be verified by anybody using only the Public Key.
If the stated Address has never received any funds, I believe that the query disappears from the network within some short amount of time.
It is common practice in Public Key Cryptography, additionally to encrypt any Private Keys using a Password which is not stored, and which the user must enter, every time he wants to use them, but not to encrypt the Public Keys. Since simply to receive an update for the Public Keys does not require the user enter his Password, it follows that the Wallet Program does not need to prove to the network, that it does have the Private Keys stored.
Otherwise, if the Wallet stores any Public Keys without the corresponding Private Key, by default, those are assumed to belong to other users, as potential Addresses to Send funds to. And this is about as much as a basic Bitcoin Wallet Program needs to be able to do.
However, most specific Wallet Programs have additional features and capabilities, specific to one Program. For example, some Wallet Programs allow for more than one Wallet to be created, and additionally allow for pure, Address-Watching Wallets to be created, which when synced, also query the network for a list of Addresses, but for which the Wallet in question does not store any Private Keys. These Wallets receive updates for the list of Addresses even though the Addresses in question are actually externally-owned, since the network never required any proof from the Program anyway, that it has the Private Keys.
I think the main disadvantage of this approach, is the fact that this separate Wallet does not get synced, unless the user specifically instructs his Program to Open that one.
But, since some programmers do not feel that their users need these advanced capabilities, certain Wallet Programs simply leave them out, especially in the case of Wallets meant for smart-phones. OTOH, smart-phone Wallets often have additional capabilities, related to being able to scan QR-codes, in order to acquire Addresses to Send To, or to acquire ‘Requests For Funds’, which in addition an Address, contain the Amount that should be Sent, within the same QR-code…