As I expected, a distributed hash table can be messed up by mischievous nodes. Kademlia is an ordinary DHT and it must be modified for security in ways like:

"The proposed KadS network is almost identical to the Kademlia network, i.e. it consists of the described RPCs and implements the same XOR metric. The major extension to the protocol is that every node is equipped with a public/private key-pair signed by a trusted CA. This extends the normal Kademlia network to a public key infrastructure (PKI) in which every communication is encrypted, every node can be trusted and only verified nodes can participate in the network." -- http://blog.philippheckel.com/2009/03/16/kads-a-secure-version-of-the-kademlia-protocol/

That's inadequate since it means trust and third party authorities. By using unique coin IDs and digital signatures for both minting and transactions, the double spend and counterfeit problems are solved, yet the problem of ensuring consistent data in the DHT remains to be solved. (The coins in my proposal are minted by a central authority but after having been minted the coins are fully decentralized and peer-to-peer.)