The vaunted peer review - supposed to eliminate problems like this - failed.
Not really. Peer review is designed to catch holes in their logic or spot errors, such as if the incorrect analysis method was applied or if their scientific evidence doesn't fully support their claim. When it comes to outright fraud, a peer reviewer really has very limited means of spotting it. In exceptionally rare cases they will request that a claim be replicated by an outside researcher, but that is exceedingly rare and I don't think I've ever heard of a reviewer actually attempting to replicate research themselves as part of the peer-review process.
What normally happens is that other people in the field will read the paper and say "I don't really buy this" and attempt to replicate it themselves. If a consensus of groups can't replicate their findings, then the question becomes whether there was fraud involved or if it was just another example of "winnners curse" or maybe something unique about their study that was different from all the rest (like if they were looking at a different cell line or global population than everyone else). In no case is it really feasible for the peer-reviewer to catch outright deceptive fraud, but usually it gets spotted sooner or later. And the bigger the scientific claim, the bigger the bulls-eye becomes on your back.