Wouldn't it be in the best interests of state sponsored hacking teams to hide or blame other states?

Of course. If I were leading an offencive team at CSIS, I'd do my best to procure machines and credentials in anorher country to launch the campaign from. Ideally a known adversary. That doesn't mean that country isn't executing their own attacks. In fact my charade wouldn't work if I chose a country that has no track record of attacks.