Yes? I don't know what you're referring to by "the news media it specifically mentions" but speaking as someone who doesn't have a dog in this fight, but who do

Yes? I don't know what you're referring to by "the news media it specifically mentions" but speaking as someone who doesn't have a dog in this fight, but who does actually want to know what's going on, it seems (to me) worth knowing that the paper being held forth as evidence that the vaccine is dangerous carries the disclaimer that it's a pre-print, not peer reviewed, and should not be used to guide health-related behavior. Is the vaccine dangerous? I would like to know! Is this paper strong evidence that the vaccine is dangerous? It is not convincing to me in its current state, though maybe it will go on to be proven a valid and important piece of work. If your point is that there is a lot of low-quality media out there, then I agree. My sense is that we should increase, not decrease, our skepticism in response.