The ScriptSig does not by itself prove Bitcoin ownership, but it is an important component of the transaction input that provides the necessary data for unlocking the transaction's UTXO being spent.
In the case of the ScriptSig you provided, the inclusion of the digital signature and public key in the ASM format indicates that the transaction input's spender possesses the private key corresponding to the public key included in the ScriptSig, and can therefore legitimately claim ownership of the UTXO being spent.
However, it is also important to note that the ScriptSig alone is not sufficient for proving Bitcoin ownership, and additional factors and mechanisms, such as the transaction's outputs, the blockchain ledger, and other cryptographic protections, must also be taken into account.
Overall, Bitcoin ownership is a complex and multifaceted concept that requires a thorough understanding of Bitcoin's technical architecture, cryptographic protocols, and transactional mechanisms to fully grasp and utilize effectively.