doublespend – Is PoW and consensus unnecessary without double spending?

Satoshi’s whitepaper claims that the reason there must be a consensus on all transactions is to solve the problem of double spend. I’m curious then, how would a non-consensus based system work if double spend were not a problem?

If a coin is still represented as a series of transactions, each of which is verifiable, and these are submitted as proof of ownership during transactions, then how can one prove that the entire coin is valid? While no one can fake a spend from an unwilling party, it seems you could fake the entire coin altogether.

The only solution I see to above is that each coin is initially issued and signed by a trusted party. Once these coins are in existence the trusted party is removed.