I don't get. Why isn't the model open if it works? If it isn't this is just a fart in the wind. If it is the findings should be straightforward to replicate.
Yes, the community should force Nature to up its standards or ditch it. Software replication should be trivial in this day and age.
(I agree with you in principle; my example above is meant to show that standards for things such as reproducibility aren't easily defined. There are so many factors to consider.)