The author of that tweet clearly has an issue with the arxiv being an open repository where everyone can upload anything. There is nothing about open access in the tweet. And arxiv is not same as the concept or movement of open access. Most articles on Arxiv doesn't even have a proper license to fulfill the definition of Open Access in the BOAI declaration.
Further proof that the authors tweet is not about or against open access is that she publishes open access herself:
Arxiv is open access prepublication, and doesn't remove the need for peer review to get into actual journals. If you apply for a grant and you say "I was published on Arxiv" you are not getting that grant.
Additionally, Arxiv won't kick you off their platform if you post a preprint there, and then you get published in Nature.
In other words, the reason it does not change the point is that Arxiv does not weaken the publication process for the actual journals the preprint will be submitted to. You still need peer review to get published and you are still incentivised to do just that.
You could argue 'preprints ARE publishing' but I'd need to be convinced of that point because I don't agree for the reasons stated above.