You've to got a reputation system with identities also stored on the blockchain, and you accept the transactions only from the most trustworthy people. Counterfeit paper currency exists, and counterfeit bitcoin (not BTC) transactions might exist, but not every person is equally suspect of using counterfeit money.
Sure, but then you aren't really using bitcoin. The whole point of bitcoin was to be a trust less system where transactions are verified cryptographically on the blockchain.
Transacting bitcoin private keys without going to the network and trusting the other party to not scam you defeats the whole purpose.
