Yahoo has a lot to lose by violating its own privay policy. The email account is a business transaction that comes with certain guarantees. The company can't just revoke those, regardless of the intentions of the family.
An account is different from other personal effects because it is an intangible thing. Unless the man printed out the messages and left them with his other things, the messages should remain private.
We don't know the relationship between the man and his family, or how much access he'd want to give them to his personal account. He signed up under a privacy policy that blocks this sort of sharing, and unless he contradicted it himself, we should assume he wanted his privacy respected.
The family may 'need' access to his account in thier own minds, but it's not thier decision.
When you install software from whoever on your computer, there is always the section that says Read the agreement and click box to agree to install or some variant of this. I have never read any of it. I doubt if the Marine did either. If you dont click yes, I agree, you don't get to continue with the installation. I would be very surprised if very many yahoo users actually read these agreements.....