1) What they're saying isn't, as you point out under #3, not canon.1) The producers and writers stating that it is
2) Blatant references to things that only happen in the Prime Timeline
3) The fact that visual aesthetics are not and have never been Canon
All of the above things "outweigh the evidence that Discovery isn't set in the Prime Timeline" because such evidence is nonexistent.
2) And? Can still be an "alternate timeline". And how can you tell they only happen in the Prime Timeline?
3) Perhaps not, but there are a few things that were established and that continued up to Enterprise. For example, the writers of the TOS and TNG were told in the respective writer's bible that the "viewscreen isn't a window". Even if the Abramsverse movies used windows, there's no reason why this show would go with it. Visual changes (such as that of the Klingons) were addressed.
Overall, I think it's a lazy show and it feels as if it only got Star Trek slapped on it and that the producers really wanted to do another Sci-Fi instead.