As I understand it, peer review simply means that the paper looks to be of interest and is not obviously wrong. As you say, peer review does not mean verification.
I think it depends on the journal. Some have far higher standards than others. Nature picked the holes in this, which is not surprising since they one of the highest-regarded scientific journals there is with a considerable pedigree. But a lot of others [like Science lol] didn't check it thoroughly enough [and that is most journals].