no, the whole point of bitcoin is that it's money and that means it has to be a global ledger, in order for its supply to be limited... it's the realisation of ideas from Mises and Hayek

there is no need for a global ledger for a server that one person is responsible for and providing for a limited set of users, it's a different structure, in terms of law, money cannot be a trust, but any enterprise can be a trust because a trust must have a bounded set of beneficiaries

any kind of "currency" that is still a trust is not money in the sense of gold coins are always going to be worth something because they are durable, portable, scarce and verifiable

bitcoin's got all of these properties