PartSkeptic
Illuminator
I haven't been following this thread but my opinion is that theists (regardless of which organised religion they support) find some solace in prayer and also experience from time to time the prayer-request being answered through circumstances.
This leads me to the assumption that if there is a god which responds to prayer then it is outside the influence of organised religion because it prefers to acknowledge something which is outside the direct influence of said religions.
Which is to say, even that organised religions are generally in opposition (or competition) with one another, it doesn't seem to matter to that which responds to the prayer...one does not have to make a request in the name of any particular god in order for that prayer to be responded to, even that this is what organised religious doctrines often teach.
Then there are those who do not believe in any particular god idea who still 'put it out to the universe' and find that they get a response to such requests also.
The argument is that such 'responses' are simply coincidence, which is just as likely an explanation as any but for obvious reasons it doesn't really matter to those making the prayer/requests as long as this method works for them, giving them the added impression that something bigger and more able than they are is 'watching over them' and assisting them with their choices in life.
For me, I think you have summed it up quite well.
But what you do not acknowledge is that prayer is only one reason to believe in the existence of God.
I concede that my prayers may be coincidental and that God may not exist. And that all the other reasons for my choice to believe (with a slight reservation) in God, may also be flawed. In fact, MUST be flawed if God does not exist.
Conversely, if God does exist, the reasons put forward by atheists to explain various phenomena ARE sometimes flawed. Unless God reveals himself rather than provide "clues" or revelations to selected individuals (the prophets), then we will not know for sure.