Take regular backups has always been good advice, that doesn't go away just because a company handles your email for you. Always take archives from cloud services just like you backup HDDs, use a custom domain to forward inbound email traffic and you'll be 100% protected.
You chose the worst example of Google being able to ruin somebody's life when if they really wanted to be evil, they'd have a monumental amount of data for blackmail, the ability to silence you online, etc..
