If your point is to use an extreme example to sway your position I'll overlook it, but at any rate. I don't understand how you can come to the conclusion based on the evidence presented that prayer didn't make a difference. The examples of this sort of coincedence are too numerous in my experience to view this as superstition.
I think that there are several different factors that come into play that cause some skeptics to speak in absolutes about negative claims.
There are a lot of claims of miracles that are demonstrably false.
There are no claims of miracles that are testably true.
There are a great number of people asserting absolute positives on poor evidence and attempting to use proper (non-absolute) counter-arguments as a lever to assert that the position of the non-miracle-believer is weak.
I don't believe that prayer has any effect on the universe that does not stem from the phyical act or subjective experience of praying (if you pray by kneeling in the grass, you get crushed grass; if you believe your praryer will work your attitude changes and may effect outcomes, etc).
It is entierly possible that prayer does work in some way I don't understand and which is for some reason untestable, or for which no valid test has been described. Given both the lack of testable evidence for prayer working, and the number of testable claims that proved false, I doubt prayer works.
I do wonder where you've done debating. You seem to have well formed ideas. Though I disagree with you on much I do respect your skill.
Thank you. I enjoy your posts as well.