I think what you are talking about is very possible. There are many examples like the ones you give. The ones that can do it seem to harness a natural law.
Everyone seems to go through a training cycle where it seems very cool to be able to do it. Then it seems to only be used when it has a purpose. Like Jesus calming the seas or Medicine Men to bring the rain, or Healers performing miracles like Edward Cayce.
Most will say that the power does not come from themselves but that they are able to tap into it to direct it. It usually has many unseen conditions that must be met to do this. Everyone develops their own method of doing this.
In the book "Rolling Thunder" the Medicine Man (Rolling Thunder) would get a stink bug and irritate it to make lightning and eventually rain. Maybe he used the bugs' frustration and consciously connected to the Great Spirit to make the storm.
His purpose was to heal the dry land by bringing rain, it was not done lightly.
Anyway, good stuff