The solution to these problems is simple.

1. "Joe and Bob - were they together on Sunday at 2pm?"

Joe and Bob avoid this by not authenticating using the same mechanism in the same room at the same time.

2. "John just uploaded a signature that matches our samples of 'Kill the president'".

Solution 1: John understands how the authentication works by recording ambient sound, and refrains from saying things like "kill the president" during that procedure.

Solution 2: John starts an Internet meme which encourages every user of this authentication mechanism to say "Kill the president" over and over again during the procedure. Now, millions of signatures match.