Does the one who provides the digital signatures makes them the owner of the private key/s?
Discussion
Cryptographically, anyone who holds a private key has ownership over the corresponding public address associated with that private key. Digital signatures are obtained by an individual in possession of this unique private key. The digital signature simple cryptographically confirms or proves to others that the intended owner can easily execute secure/valid transactions utilizing some cryptocurrencies available as resources.
Digital signatures greatly improve transaction security as it deters possible external malicious actors from tampering with seals provided to Public Blockchain ledger containing sure metadata autonomously recording exchanges onto inaccessible blocks afterward kept there for eternity-chain modifications require re-validations across multiple intervening unlinked chains/tasks so impossible through mining nodes\ verifying agents currently supported sufficiently comprehensive P2P distributed cloud networks.
As such, any individual providing digital signatures (generated with their owned and securely stored private keys) is considered the owner of a known access node to underlying fundamental addresses having said abilities retained within those locations.