True. However most people have a work account for business matters and a personal account for everything else. If you had used a .gov account exclusively for all gov't correspondence, I wouldn't care about a personal account. You didn't. Hand over every email sent or received on that account. You created the problem, deal with the consequences.
Very correct you are sir. I work for the VA. Any correspondence that I have concerning VA work is conducted on a VA system. I am not allowed by penalty of law to conduct VA business on a non VA mail system.
The VA does not care if I conduct private business on a non VA system. The VA also informs us that any communications I conduct via their system even though it be to a private system such as Yahoo Mail, G Mail, etc. is not private nor confidential. It is not confidential because it went to a private provider via the VA system.