Peer review definitely could and should have caught the fake data in this case - there were too many implausible things about this paper that one could verify with a google search and see cannot be right.

In fact, it took people about one day from publication to start pointing them out with proof - and these people were (supposedly) less qualified than the peer reviewers.

It is true that, with properly faked data, a reviewer cannot be expected to catch it. Nor can p-hacking generally be discovered from an incomplete description.

But quite a bit of faked and even p-hacked data is less-than-competently done in a way that a reviewer can and should be able to catch;

And observational data or meta-study are much easier to verify, since no experiment was done by the researcher either.