I agree with checking the references, but again, my point is that as a general rule it's really not that easy. You can think it's easy because you have had the work done for you for this particular article and that it is obvious in this particular article, but in general, it is way more complicated.
Properly checking that the citation is indeed saying that often requires studying the quoted paper quite in details. Again, it may not have been the case here, but it is an amount of work that a reviewer should plan in advance.
But more importantly, and it makes your point moot: if the article is misrepresentating the reference, then, rather than in the peer-review process, it will be the reference author that will notice it.
I think it is my point: people here are seeing peer-review and are thinking that it is the ultimate method to decide what is good or bad (or what is "consensus"). This is ridiculous. A peer-reviewed article has NEVER been considered as "obviously correct and uncriticable". A peer-review is just one of the step in the long process. If indeed the references were not saying what the article is saying they say, it will end up being discovered.
The peer-review is the first step before submitting the article to the whole community, and it is then that the majority of the discussion happens.
> If you're not double-checking dubious claims
While I agree with the previous things, this bit makes me pause: careful with that, historically, the majority of correct claims were, at first, sounding dubious, and the majority of incorrect claims were, at first, sounding totally not dubious.
Let's rather say: let's double-check everything.