Just because a prayer preceded an event, doesn't mean that it MUST be false because it preceded it.
Seems fairly obvious to me.
For example, I coughed and then I found spit on my monitor. Does that mean it's post-hoc?
Yes. Post hoc means 'after this' so it would be. The fallacy is the notion that just because one thing follows another doesn't mean they are causally related. You need more information to know if they are causally related. Thus for prayer "I prayed and I got better. The praying made me get better" is the fallacy of post hoc ergo propter hoc.
It MIGHT be that the prayer got you better, but the only evidence to base our reasoning is that getting better happened post hoc.
Therefore, if all prayers are genuine, then they are still regarded as post-hoc because we can't prove it.
Not at all. All things that come after things are post hoc. It is a fallacy only when you assert that the reason something happened was because of an event which preceded it, with the only reasoning being that the preceding event happened first.
If you can't actually demonstrate that prayer worked, you
can say I believe that prayer did this.