I believe this is a public perception problem. The reason that a troubling number of people no longer believe in science isn't that scientific method is flawed or that people don't believe in scientific method. The bigger concern is the way that scientific studies are mounted, paid for by interested parties that have conflicts of interest to produce results favourable to a desired outcome and then they're presented as science instead of politics.

When one can't trust the information they're looking at without having to dig into the political backing of the study and the results and without having to wonder which outliers have been trimmed to further hammer home the point of the stakeholders, we're no longer looking at science, we're looking at propaganda.

So the problem isn't science. The problem is the manner in which science is being subverted for financial gain. That's not science.

This is why science is losing credibility and authority outside of scientific circles.

If you want credibility and authority, you have to not only act with integrity, you have to be seen to be acting with integrity. It does't matter how honest your study or how objective your results, if people look at your study and see that it was funded by Monsanto and makes Monsanto look good, it looks like Monsanto paid for a study to make Monsanto look good and therefore it's biased and can be ignored.

This is life. If you want to be seen as having integrity, you have to act with integrity. And when people who were already distrusting of the way science is presented in the media are being told that they can't trust the media by authority figures, as ridiculous as those authority figures may be, eventually people stop listening until the furor abates.