A neurosis is an unreasonable response to perceived reality which may indeed, as you say, not be what it appears. Solutions for neuroses must lie with the neurotic not with the stimuli held to be 'responsible' for them.
In 2013, a story made the front page of HN about high lead levels in imported rice (covered by some credible sources). For a few weeks, as a precaution, I avoided giving my children rice to eat (and I'm sure I wasn't the only one) and getting into a fairly heated argument with my spouse about it, who thought I was crazy. It later transpired that the entire story was based on miscalibrated equipment. Till today, there are news sources that haven't corrected the story (Google "lead in rice"). This was an extreme example, but I don't doubt that a lot of health stories suffer from real flaws, but are tougher to debunk.
Science is important, but science reporting (especially medical reporting) seems awful. No parent wants their child to be harmed, indeed, I've read comments on HN where people say they give their kids glass bottles because of the putative risks of phthalates. While I don't blame them for being careful, imagine what happens when the glass bottles shatter? It is very tempting for parents to panic and to "parent by headline", and it is obviously profitable for researchers and their institutions to generate maximal alarm. However, HN is my primary source of tech news, and I would prefer it if it wasn't clogged with possibly dubious health stories which perpetuate this cycle.
I don't think it's limited to science reporting. The more I learn, the easier is is to see the numerous errors made by journalists across all areas. Take Vox, it's an older link but they have been criticized for poor accuracy in reporting (and failing to prominently note corrections).[1]
The Royal Society has it right with their motto, nullius in verba: the news media, much like Wikipedia, is not a reliable source for facts.
[1]: http://theconcourse.deadspin.com/46-times-vox-totally-fucked...
Yes, and its corollary and my personal favorite...
I know I'm paranoid, but am I paranoid enough?