Peer reviewers can't check everything, especially when the conclusion results from elaborate analysis of data from complex apparatus. Sometimes you detect bonehead mistakes, but usually your focus is more on clarity than correctness: do the authors explain their methods and reasoning in enough detail that someone else can repeat the research?
Yes, I agree with you here about referee's role, but not about authors role. It is necessary but not sufficient to explain methodology so anybody could repeat it. It is necessary also that if repeated the measurement from the paper, the same results are obtained. The one of many reasons is also so that other people do not have to repeat often expensive measurements.
But this is not fraud, and perhaps it's even healthy. Better to get crazy results out there than bury them in notebooks: sometimes they turn out to be major discoveries.
So for instance, when some not sufficiently checked results for medical treatments get published, you'd say that this is perhaps healthy?
Absolutely yes! It is the physician's responsibility to avoid basing treatments on results that haven't been independently confirmed. It is the researcher's responsibility to publish: how else will you get that independent confirmation?
In science there is no such thing as "independent confirmation". The whole point of publishing an academic scientific paper is to have an independently obtained results that are claimed in the paper. Imagine only that we have to "independently check" results obtained in particle accelerators.
Recall how the "neutrinos faster than speed of light" claim ended: not by imaginary independent checks but by finding the error in measurement, which, among other things, saved work and money of people to further the research in the direction that is now very likely would have led nowhere. If someone is still crazy enough to study speed of neutrinos in order to prove that they are faster than light and then finds that they are indeed faster than light, well that still would not make the previous measurements correct.
How about claims? Would that not confirm at least the claims of the former paper? Yes, but the science is not about claiming claims.
Other researchers need to know what they should attempt to confirm or falsify.
I disagree, and this has to do also with the referee's role: one of the reason the referees are not supposed to confirm or falsify results of the paper they refer is exactly because it is understood and expected that the authors have tried to do so themselves, to the extent that the field is requiring.
We're talking about the science of the journals here. This is raw "source code", checked to some degree, but not debugged. The debugging takes place in the community: if you don't publish, your results will never get properly debugged.
So from my responses so far now is hopefully crystal clear why your approach to doing science and the view of the role of scientific journals is not only non-scientific, but also socially dangerous.