I'm facing a similar problem with a competitor - the main content of their homepage is basically just a *big* list of model names and numbers of the widgets they supply in a 10px font (effectively keyword-spamming). Majestic reports a big spike (almost overnight) in the number of backlinks a few months ago from approx 100 ref. domains to 1000's of ref domains, all from thin content blogs, directories and even link exchange sites!
To make matters worse, their site uses a tables-based design, has *no* title or headings tags, has image based navigation, takes 25s (yes, that's twenty-five seconds) to load the 2.5Mb homepage, makes over 200 http requests, a page speed score of 52 (not that really means anything) and has over 450 validation errors.
And yet they consistently rank higher than any of the more deserving websites in our niche.
(ps they're not a "brand" or one of the big boys, just an independent ecom store)