That is not how science portrays itself; that is how the media portray science.
Science is a method, not a body of knowledge. There is a body of knowledge that is
scientific, but even if all of those facts and observations were erased (tragic as that would be) the method would still exist.
That said, science certainly appears rigid, if you do not understand--or are philosophically opposed to--the idea of testing our assumptions. If you are a fan of, say, homeopathy, an alternative "medicine" that flies in the face of medical knowledge and has been proven not to work, then in order to support that belief, you must either be ignorant of where science stands on the topic, or you must reject it as a method of inquiry.
The problem is, though, that if you reject science as a method of inquiry, you have essentially excused yourself from any possible reasoned discussion.
As to the question of coincidence, I recommend this video:
http://www.youtube.com/watch?v=98OTsYfTt-c