Infringement depends on permission. No third party can possibly know whether or not the use of a given work was authorized or not unless told by the copyright holder.
Now, when told by the copyright holder that no use of some work is authorized, they can flag all copies of it that they are able to find and match it under the assumption that nothing is authorized. But you couldn't add anything if we assume that every user is lying about being authorized.
Moreover, as was demonstrated in the Viacom case, even the copyright holders get it wrong. In particular, Viacom had uploaded copies of their own works and made them appear leaked. Yet these were uploaded by Viacom itself and, thereby, authorized. They even had to go back and have them put up after taking them down by mistake. And they had to remove them from their complaint after being told of their mistakes. Twice. After doing due diligence with expensive lawyers.
Now, when told by the copyright holder that no use of some work is authorized, they can flag all copies of it that they are able to find and match it under the assumption that nothing is authorized. But you couldn't add anything if we assume that every user is lying about being authorized.
Moreover, as was demonstrated in the Viacom case, even the copyright holders get it wrong. In particular, Viacom had uploaded copies of their own works and made them appear leaked. Yet these were uploaded by Viacom itself and, thereby, authorized. They even had to go back and have them put up after taking them down by mistake. And they had to remove them from their complaint after being told of their mistakes. Twice. After doing due diligence with expensive lawyers.