Yes, you can run your own Etherium node and server, and connect a MetaMask wallet to it.[1] As Moxie points out, nobody wants to do that.
Worse, the blockchain does not, apparently, contain the hash of the data. You can't even prove you even have access rights to the data if the hosting service goes down. All you own is a link to a URL.
There are more Ethereum full nodes than two, but how many will accept web queries? That's a service.
[1] https://media.consensys.net/how-to-install-and-synchronize-y...