on a personal note, i do not think governments invest in bitcoins secretly because it's a decentralized peer to peer transaction with no central authority and also it can affect the country's fiscal policy, business and also help to facilitate crime rates.
Why do they need to hide if they want to support bitcoin? Bitcoin is not illegal and any people can buy it. In short, there is no restriction whether you are poor or rich, young or old and official of government or not. They don't need to have secret even there is anonymity. They are just humans.