Lots of people who are pro-science don't understand science. Lots of people do understand science to some extent. You apparently don't have a full understanding, since you insist on controlled experimentation. Science is a process of observation (which can be greatly assisted by experiments) and making models that will predict things.
Your view of statistics is slanted. It's possible to prove anything with any form of reasoning, provided you can slip in the right assumptions. Statistics isn't unique in that. Statistics is a very useful tool, and can be used rigorously. (You are aware that the laws of Thermodynamics are purely statistical, aren't you?)
The idea that science makes God obsolete is not a problem with science, but with religion. If religious leaders make claims that can be shown to be wrong on scientific principles, then refuting those claims is going to make the rest of their message so much less convincing. One example would be the belief in some loudmouth fundamentalist US churches that evolution didn't happen: when somebody from that background actually looks into evolution and its evidence for himself or herself, the whole body of the teachings of that church is up for serious questioning.