The authority of science is based on the trust that is vested in the peer review.
I am speaking about science the method, where the only "authority" is empirical evidence gained through repeatable experiments. The authority you are speaking of is the institution (or community) of science.
Peer review is not a fundamental part of the scientific method. You are more than welcome to distrust all peer reviewed research and attempt to repeat or falsify the results yourself. Strictly speaking, the scientific method demands that we do just that, but we generally don't because it's highly impractical.
The hypothesis that peer reviewed science is true science, is falsified if even only 1 example can be found in which the theory isn't true.
I'm not sure what you mean by "true" science, but it seems that you have switched to another common meaning of the word, which is science the accepted body of knowledge. Just because something has been peer reviewed doesn't mean it automatically becomes a part of scientific knowledge. In other words, you're right, the hypothesis is false, but it's not the revelation you think it is.