they were trying to statistically relate instances of events happening to this case because, according to the op, some people act like those instances happening is absurd.

OK, assuming this is correct, the logical fallacy being employed is a straw man. I have never seen anyone claim that it's absurd that Jay falsely confessed because false confessions don't happen. The argument is that this case does not appear to be a false confession based on the facts and circumstances.

But, did the OP really "statistically relate instances of [false convictions] to this case"?

Let's use your construction "x is possible because x has actually happened." You just said something is possible because something happened. In other words, "X exists because X exists." That is a tautology. The post is meaningless unless there is some argument showing why it is likely that Jay falsely confessed, and that is not going to come from the exoneration database. It will come from the facts of Adnan's case.

Now the OP does claim that Jay false confessed to avoid the death penalty, but that doesn't make sense.

Look at the exchange here:

https://www.reddit.com/r/theundisclosedpodcast/comments/3kyqj6/episode_11_the_deals_with_jay/

From CM:

If Jay was an accessory before the fact, which is what he said in his police interviews, he was guilty of murder.

From Susan Simpson:

Nope. He confessed to murder. I don't think he realized that's what he was doing, though

So, Jay confessed before he thought he could be on the hook for the death penalty. Oops.