I don't understand how negative SEO could not exist. Google is cracking down on people buying back links right? If I bought links for a competitor's website, wouldn't it stand to reason they'll be punished? Google has no idea who is doing the purchasing. (You could replace buying links with any action Google' algo punishes.)

As long as Google's algorithm has punitive measures in it from something that happens off of your site, it stands to reason a competitor could do those things on your behalf.