It doesn't, but platforms basically do everything they can to claim the various common-carrier liability shields in DMCA-like laws. In the U.S. that means they forward the takedown request to whomever generated the content, and in theory should allow that generator to comply, or publish a counterclaim.

The whole system falls on the floor though when the common carriers aren't, and have low quality processes that don't actually enable the counterclaim half of this process.

The entire concept of a "takedown request" is a compromise solution. Platforms would ideally like to be a public square, where third parties can say whatever they want and the platform doesn't have to do much about it. Copyright holders, revenge porn victims, etc. would prefer to hold the platforms strictly liable, because on the Internet it's extremely hard to actually find the third parties. So in a variety of contexts we've found it's useful to meet in the middle: platforms are exempt from liability, but in return they have to process takedown requests, unless the third party challenges the takedown and makes themselves available for possible legal proceedings.