RE: authenticated email

If message contains the public key of SMTP (which could be made-up), the
internet header and message is signed.

If public key stated does not encrypt the message digest. This would
mean it has been tampered/modified. 

If the public key stated is correct, when it verifies the message
digest. The message digest will include the message and the internet
headers. If this is successful, you certain trust the internet headers
which can used to trace.