I don't think the approval process is being used to enforce rigor in general, the (claimed) problem is the paper lacks rigor specifically in regards to claims a

I don't think the approval process is being used to enforce rigor in general, the (claimed) problem is the paper lacks rigor specifically in regards to claims about google's behavior. Publishing a paper with a lack of rigor about some obscure mathematical technique isn't a problem for google (beyond some possible but unlikely mild reputation damage). Publishing a paper with a lack of rigor that says google is doing unethical things, when those things are questionably accurate, that is something google would (and should) have a problem with. Whether the paper actually lacks rigor in a relevant way is not something I can comment on.