If you don't have a lot of experience in the field thinking you can do better original research or synthesis than the experts is probably not reasonable.
You don't need to hold that belief to think that the experts are wrong. The expert might be wrong because they are willing to downplay the risks associated with vaccination because they think the benefit from higher vaccination rates outweigh the cost.
There also a huge commercial interest in the experts supporting vaccination.
Experts can be wrong and it's often useful to read papers yourself.
Vaccination is probably one of the hardest topics to have a rational discussion about. I have some reason to believe that the author of http://whyarethingsthisway.com/2014/10/23/the-cdc-and-cargo-cult-science/ is someone interested in looking for the truth, not winning a side - at the very least, I'd like to help him when he says this:
I'm getting started on reading the actual papers, but I'm hoping this finds someone who's already done the work and wants to go post it on his site, or if not, someone else who's interested in looking through papers with me - I do better at this kind of work with social support.