If Sergey Brin thinks the current medical research establishment stifles certain kinds of research avenues, fine. But let's not cast this as him "proposing to bypass centuries of scientific epistemology in favor of a more Googley kind of science". He's not the next Francis Bacon, and this isn't some deep insight into the nature of science.
I think he is not proposing anything substantially new. Collecting data before formulating your hypothesis is the norm, not the exception.
First you see an object fall and them you wonder why. The same applies to birds flying, wood afloat, fire, atmospheric pressure... we observe(collect data) first, we make assumptions and look for more data later.
BUT, never underestimate the power of a GooglePlex for gathering and analysing data(like generic one). Never before we had used it, and so we could see things we never did before.
You know what happened when a man without studies created a miscroscope. The "scientist" of the time said that he didn't knew Latin, so he could not be called scientist, and that the microscope will only work for seeing the same things we already know bigger.
Because combing through large amounts of data in search of a hypothesis is as old as the hills. (In fact, the dangers of generating false hypotheses were already detailed on HackerNews a few days ago.) Brin isn't proposing some new way of doing science, he (I think) is just suggesting that the current mentality/funding-structure/whatever is not set up to support this type of analysis optimally.
Because he's not suggesting an experiment. This method involves taking data already obtained and doing analyses on it, to look for something, it's really a different way to form a hypothesis. After he finds something this way it'll go "back" to the standard rigors of the scientific method.