The discussion was around trustworthy data, so I think they want proof that a page served up and stored was in fact the actual page served up and stored, for later audit. HTTP doesn't give you that. Bittorrent doesn't give you that. But blockchain can, if you pay a fractional coin to store the hash of the page in the chain forever. With a reference to the page and to the transaction, you can then later determine whether the page is intact or has been modified. And for bonus points a signature could be stored as well.

This is just passing the overhead cost to whomever is mining the network though.

The trustworthiness of a blockchain comes from it's ability to repel attacks with computing power, with more power meaning more trustiness. This means tremendous overhead for a blockchain that could just as easily be performed with the centralized system we have now.