Indeed it doesn't. 51% attacks don't allow you to steal something you've never owned, because there's no valid transaction that transfers ownership to you.
The only way a 51% attack allows you to steal anything is by reverting a transaction you made that sends something from you to me, and immediately replacing it with a transaction that sends the same thing from you to yourself.
This is only useful if you convinced me to give you something in return for the money you paid me in between you sending the original transaction and subsequently reverting it. Once all is said and done, even if I can't prove it (for some definition of proving it), I still _know_ you stole from me, which has its own consequences.
51% attacks _do_, however, allow you to wreak havoc on the chain state, which can sometimes be an attack worth performing.
You can prove it, you have the signed transaction from him that can't be included in the blockchain because their inputs were spent. If you know who you were dealing with that did the double spend, you likely would have a very good case against them of fraud.
There's two potential issues: Can I prove they control the private key that goes with that transaction? Can I prove that that transaction was originally used to settle a specific invoice (or something equivalent)? Sometimes, one of the two will be true and I have a strong case. In others, I have neither and it's my word against theirs.
The only way a 51% attack allows you to steal anything is by reverting a transaction you made that sends something from you to me, and immediately replacing it with a transaction that sends the same thing from you to yourself.
This is only useful if you convinced me to give you something in return for the money you paid me in between you sending the original transaction and subsequently reverting it. Once all is said and done, even if I can't prove it (for some definition of proving it), I still _know_ you stole from me, which has its own consequences.
51% attacks _do_, however, allow you to wreak havoc on the chain state, which can sometimes be an attack worth performing.