We know that light is distorted by knowing the astrophysics of the source of the light. Stars have spectra that appear a certain way. Supernova spectra are also known. Ditto spectra of cephid variables, neutron stars, gamma ray bursts, and a whole host of other astronomical objects. When we see distortions in the light from these objects, we know because we know the process by which that light was produced.
Don’t get me wrong: dark matter may well turn out to be wrong. It’s not enough, though to just say it is. You have to provide evidence that it is. That evidence, right now, would best be delivered in the form of a coherent alternative model that explains known observations. Dark matter, whether you believe in it or not, does explain a fairly wide range of astrophysical and cosmological observations. A better model might well explain those observations, and others, better. It’s not as though scientists haven’t considered alternatives. Many on this thread believe that modified gravitational theories are the answer. However, these have been studied pretty extensively (look up the acronym MOND, which stands for modified Newtonian dynamics if you are really interested). Right now, dark matter is the best model we have.
I have been somewhat disconnected from the cosmology field for about a decade, though I am very interested in it. I have looked at a couple of MOND sites discovered in search, but I am not satisfied. Can you recommend two or three for me to reconnect with this subject? (High math level is OK, and even desired.)