You added that last bit, yes, the explorer, which is easily read. It is indeed served up by anonymous people who check it via cryptography, to verify that the Proof of Work was done at every block. These anonymous people come to a single consensus, yes, true. HOWEVER, the LEDGER that is the blockchain, is easily readable right back to the creation of the coin, so you can see clearly the coin's integrity.
Not just verifying the proof of work, the signatures need to be verified as well, otherwise those blocks might contain invalid transactions making your coins worthless. That's hard core cryptography using actual math. It is essentially the same situation as crytponote, just slightly different math.