In a series of papers, Santilli and collaborators released various strong statements against the general theory of relativity (GTR) and the standard ΛCDM model of cosmology. In this paper we show that such claims are due to fundamental misunderstandings of very basic concepts of gravitation and cosmology. In other words, we show that Santilli and collaborators demonstrated nothing. In particular, they demonstrated neither that the GTR is wrong, nor that the Universe is not expanding. We also show that the so-called iso-gravitation theory (IGT) of Santilli is in macroscopic contrast with geodesic motion and, in turn, with the Equivalence Principle (EP) and must therefore be ultimately rejected. Finally, we show that, although the so called iso-redshift could represent an interesting alternative (similar to the tired light theory historically proposed by Zwicky) to the Universe expansion from a qualitative point of view, it must be rejected from a quantitative point of view because the effect of iso-redshift is 10 −6 smaller than the effect requested to achieve the cosmological redshift.Paper dedicated to the 80th birthday of Ruggero M. Santilli, hoping that this will permit Santilli to understand how GTR and ΛCDM cosmology really work and, in turn, will permit him to withdraw his very wrong claims in gravitation and cosmology.