Don't blame the science - this is about taking science's name in vain and claiming something is proven when science has always been very up front about the limitations in what, for want of a better word, is called current knowledge. This is what always happens; people don't understand how science works or how scientists think and communicate. When the scientist says 'To the best of current knowledge, eating eggs is probably bad for you, although we really haven't researched that enough' it translates into 'Science says egg is bad for you'.
To be fair, there are PLENTY of scientists and studies which actively promote their results by emphasizing aspects that go beyond a reasonable interpretation of the data. It may be less common in "hard science" fields, but in "soft sciences" and things like nutritional studies, you'll often see "Discussion" sections at the end of the paper that claim, on the basis of some questionable stats and a sample group of 12, that they have discovered eggs are bad for you, found a cure for cancer, and suggest possible locations for the body of Jimmy Hoffa.
Okay, I exaggerate a bit. But I've literally had this exact conversation about an egg study in the past couple years with a vegetarian friend who started posting alarmist things on social media concerning eggs -- according to this recent study she read, eggs really WERE bad for you, and in her vegetarian diet, this seemed to be something to worry about since she tended to depend on eggs as a protein source.
Anyhow, I went and looked first at the press release she linked to. Not only the university promoting the study but the researchers themselves were quoted as saying almost verbatim, "There's been some question about this in the past, but we've shown here that eggs really are bad for you." Sure, there was some minor disclaimer at some point saying, "Further research is needed," etc., but the folks doing this study clearly had an agenda, which became clear when you read their paper.
I don't know what the agenda was -- maybe the director of the study is a militant vegan and hates the egg industry, or maybe they became convinced that eggs were terrible years ago and are fighting to hold onto their hypothesis, or maybe they just don't like eggs.
Or maybe, like many researchers, they just need grant money to keep their jobs or get tenure, and they want to draw attention to their work.
Regardless, the study clearly was full of holes, both from statistical perspective and a design perspective. The sample size was small. They didn't try to control for most obvious confounding variables (like, for example, what else did the people eat in their diets -- it wasn't even mentioned). Etc.
Look -- I agree with you that media reports tend to exaggerate science and often don't hedge as much as real scientists do. What you fail to account for is that some scientists often want their work to get attention (or are really proud of their pet theory or whatever), so while they may hedge officially in a sentence here or there, they may also be happy to have their results as broadly interpreted and cited as possible. And when they write up a press release or are interviewed, yes, they'll say "We still need further research," but they'll go on to provide all sorts of sweeping conclusions that their research may "suggest." It's no wonder then that media sources get confused.
(Again, I'm NOT saying all scientists are like this. But if you start reading things like discussion sections in nutrition papers, you'll quickly realize that (1) humans are complex systems, so designing a good experiment and analyzing the data fairly can be really hard, but (2) that often doesn't stop researchers from overstating the possible importance of their results significantly.)