When using deniable authentication (e.g. Diffie-Hellman plus a MAC), the recipient can verify that the email came from the sender. But they can't prove to a third party that the email came from the sender, and wasn't forged by the recipient.
However, Bob can't prove to the world "Alice sent me this message saying she hates cats!" because everybody knows Bob knows the same secret as Alice, so, that message could just as easily be made by Bob. Bob knows he didn't make it, and he knows the only other person who could was Alice, so he knows he's right - but Alice's cat hatred cannot be proved to others who don't just believe what Bob tells them about Alice.
But seriously, in a case before a court or jury, wouldn't there be much more evidence? Down to your own lawyer sending a complete dump of your phone with all those Sandy-Hooks-conspiracies and hate messages to the opposing side?