First, the notion that anyone could "peer-review" software for correctness is obviously absurd. We know this is an impossible standard. We accept that software is a (probably buggy) model, and (in my experience) reviewers are therefore extremely skeptical of results from computer models -- to the point that they're actually biased against publication. And since reviewers know that they can't verify correctness, they tend to look for theoretical papers that very closely reproduce experimental results.
Second, this type of critique is pushing hard on a straw man. The implicit assumption is that each paper is a stand-alone morsel of truth, and that the peer-review process somehow guarantees a paper's claims. This is not the case, and no scientist believes it to be true. It doesn't matter that peer review fails sometimes, because the system doesn't depend on it being flawless.
Science is about process, not people. Peer review is an important part of that process, but it's openly acknowledged that review has flaws. Thus, ask a scientist about any particular paper, and while s/he may be enthusiastic about the result or the theory, you'll almost never hear a scientist take the paper for granted as fact. More often than not, discussion of an interesting paper will center around designing other tests that can independently reproduce the paper's result. Ultimately, you have a system where a lot of genuinely smart, skeptical people are attacking ideas from all sides until either a consensus emerges, or the idea is destroyed.
The "skeptics" have it wrong, not because they're incorrect about human nature, but because they're attacking a fictional vision of science that exists only in their minds. They imagine a world revolving around a theory that is supported by one piece of data, extrapolated by buggy computer models, and presented by corrupt individuals who (for some unknown reason) have an incentive to doctor the results in the same way. In reality, science is massively redundant and competitive, computer models are treated as ancillary data (at best), and individual corruption is exposed by the redundancy of the system. If the "skeptics" put as much effort into understanding the science they critique as they do trying to find "smoking guns" for individual researchers, they would understand this dynamic.