Apparitions from heaven???

[GrandizerII]

No, not everything. There are still a couple of original points you haven't addressed at all throughout this thread. And a few other points as well in the link I provided.

The only thing I can think of that I have not addressed was the part of Poca's conspiracy theory assertion that perhaps someone was able to predict the weather for that day and saw that the sun would do something extraordinary, and told the children to say the Virgin Mary would perform a miracle. 

The thing with that theory is that the children's claim that Mary would do something on October 13 at noon came 3 months before it happened. No way to predict the "weather" (if you even want to attribute the sun changing colors, zig zagging through the sky, and drying up clothes in seconds to the "weather") 3 months ahead of time. Especially back in 1917.

Ok, but as multiple suggestions have shown, the "weather" need not be so remarkable that it could've only happened on that one specific day. People flocking to that area needed only to be preconditioned to see the expected "miracle", since the experience of the "miracle" depended on exactly that (judging from the fact that not everyone there actually saw the sun dancing around in a pinwheel fashion or whatever). In other words, they could've experienced the "miracle" on any other day and time as long as they were told what to expect and so long as the circumstances were adequate for such psychological phenomena to occur (as much as you disagree, hysteria is playing a big part here).

In addition, these accounts may have been exaggerated as well to make it sound more remarkable than it actually was. People do this all the time when telling stories so it's not an implausible thing for them to do. For example, you said their clothes were dried up in seconds. This, to me, could have easily been an exaggeration.