You would have to do a serious series of experiments to rule out all other possibilities, but scientific evidence of miracles would be enough to get me seriously considering the god hypothesis.
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Oh, so you were asking what evidence would "tell against my theory" as in what would demonstrate that it really was a miracle vs. what I suggested about lack of medical understanding?
I have a feeling that most of the people reading this site already understand everything in this article, but it's a useful synopsis of common issues faced when trying to have a reasonable discussion with laypeople, and might be good to point them to if necessary.
http://thoughtcatalog.com/2011/how-to-have-a-rational-discussion/
I also want to mention how much I wish someone had shown me something like this as a teenager- I was very prone to lecture others against their will- as it might have saved me a lot of grief. I'm curious to see if these tendencies might have been common among members of this community growing up, so please comment to tell me if so (actually, please tell me even if not-no reason to encourage my own confirmation bias)!