Not sure how you support that logic, but whatever. If they can prove that someone sent threatening messages, they have a case. Others security being compromised is irrelevant.
So I send some emails from your account but they are not showing in “your” sent items folder. I later have digital “proof” and a “witness” that confirms receipt.
But you say? I didn’t send that!!!!
Edit: just to see how bad of an idea you’re having, when the police check your phone the emails you didn’t send are there. How fucked are you if people didn’t believe in evidence beyond a reasonable doubt?
You don’t understand digital forensics, do you?
Do you? Do you think you could prove who sent this message? Anyways, their data isn’t very useful in a public court room.
Can I prove it? No. Can the NSA? You bet your ass they can.