Some "sent mail" I have sent has been important for years. I save sent mail both for information and for CYA; important stuff that somehow never got into product documentation, or something someone says I told them to do something (which I didn't) and I forward the (saved) mail in which I explicitly say DON'T DO THAT, generally ends any argument.
Of course that can be faked, but I've never had anyone claim I faked the sent mail I saved. And since everyone knows I save all my mail since the Beginning of Time (or as close as I can get to that), I don't think I've ever had more than a couple "you never said" arguments.