I agree, but I would add that if JMK is delusional or otherwise mentally ill, I won't second-guess his inaccuracies b/c it could be the result of that. OTOH, you're right; common sense says it doesn't fit. Without major physical evidence contradicting his OWN statements, he can't be the man.
Correction; sorry,
I'm not certain they've got their guy but I agree that your points do make sense.