Actually that's pretty much the case with current physical bitcoins. The only thing stopping someone from cloning coins is the risk of discovery via dual-spending. If it starts happening big-time, then trust in physical bitcoin as a day-to-day currency will evaporate (not that its much used as that today, given the 1BTC minimum denominations).
PS Actually that might work as a scam. Sell physical bitcoins cloned from original ones, but one clone only per coin. Wait a few months then cash in all those private keys (less any that have been already used by the recipients). Profit.