Well...probably not the oldest. But one of the most insidious, it certainly is. This is absolutely a fallacy. What Tim seems to want to say is:
1. (For all x)If x is religious, then x is mad
as one of his premises. But that's what he also seems to want to prove, so he clearly cannot do that. That'd just be circular reasoning. So instead, he goes:
2. (For all x) If x is mad, x is religious.
That's the reason for the bit about how people with schizophrenia are all (mostly) focused on religious figures. We are supposed to accept 2 as a reasonable premise, which maybe it is. I've only known a few individuals with psychotic delusions, but they all seemed to think they were talking to angels or yakshas or whatever. So let's say I buy 2. But then Tim still needs to prove 1. How can he do that? Well, he really cannot, but he tries to get close by affirming the consequent of 2:
3. x is religious
4. therefore, x is mad
Going the wrong direction on the conditional, and then I guess the idea is to treat inference like a conditional. Actually, I'm not so clear on this part of the strategy, but in any case, what he wants is 1, which is: (For all x) if x is religious, then x is mad. But obviously, three of these moves (1, 3 and 4) are fallacious, so it's unclear how he could reason toward the needed conclusion.
Anyway, that's the logical territory as I see it. It's basically the same deal as when opponents of pornography point out that all the rapists in prison in the Unites States looked at porn before they started raping, and try to conclude that therefore porn is bad because it causes men to rape.