I have an idea of file sharing system, which does accept files from users and distributes them to file hostings and neither does store them after that, nor gives out links to download temporary files from this hosting, storing only the statistical data, user comments and links to files uploaded somewhere else etc.
Would such a site break your ToS. On the one hand - yes, it's some kind of file hosting, on the other - it does immediately remove any file and doesn't provide download links.

TIA, PF.