Can Governments interact with the Ethereum token?

I want to buy a car using Ether tokens. The government tells me they cannot validate this transaction because they are not part of the Ethereum network. Seller of the car also has an Ether wallet and WANTS to recieve Ether as payment.

Can my government develop a smart contract that interacts with the Ethereum network? The purpose of this contract is to get a government stamp on the transaction between between buyer and seller.

1) How much will it cost my government in gas fees to validate this transaction?

2) Is my idea even possible?