Even if you have someone saying they own both private keys, and you have signed messages saying the same, there is a chance this is not true.
That's correct A signed message like this won't prove ownership, it proves that the person has a way of getting a signature. For example a custodial wallet like Coinbase could let the user sign a message from the address in their account but they do not own that address, Coinbase does.
I could also send you a PM suggesting that we should both sign messages saying that one of our addresses belong to the person as the other's addresses. If we both signed messages like this, it would not make it a true statement, as your addresses do not belong to me, and my addresses do not belong to you.
There really isn't any level we could use to say it is "confirmed" then. When it comes to blockchain analysis everything is loosely defined and the companies sell even the weakest link as a solid proof to their customers to make money!
Like I said, it is not possible to know with 100% certainty. It is even possible for two people to generate the same private key, for example if they both used flawed RNG, or if they both created a poorly constructed brainwallet (there is even a very small chance two people generated the same private key using strong RNG, although this is
very unlikely).
As I noted above, most consumers of blockchain analysis do not need to be 100% certain in order to take action based on said analysis. They are not subjecting themselves to massive losses if the blockchain analysis makes an incorrect conclusion.