I've seen plenty of sites rank high for competitive terms and their link profiles are weak if you only count Followed links.
I don't fault you for arriving at that conclusion. It's entirely reasonable. It's hard to disagree with what one sees with one's own eyes. You seem the rational and reasonable type so I will give you some rational reasons why the rankings you see are not from the no-followed links.
I've already described to you why "trust" and "relevance" do not flow from a nofollowed link. It is established and understood that nothing is flowing from the nofollowed link
So we have to ask, if nothing is flowing from the nofollowed link, then why is there a site with predominantly nofollowed links in the SERPs?
1. You may not be seeing their entire backlink profile. I have yet to find a tool that can unravel all the links pointing to my sites. And if you are relying on the Google backlink search then forget it. Google's backlink searches have always been a sample and they have become worse. You're better off in doing a verbatim search for the URL (instances where the URL is published online) as well as a search for instances where the company name is mentioned.
I'm serious, verbatim searches for company names are the new backlink search.
2. The barrier to competition is low in certain aggressive niches. What that means is that certain niches can grow aggressive and rely on certain techniques, such as multi-hyphen domain names all under the control of the same person, massive reciprocal links, paid links from poor sources, inbound links from templates, that kind of thing. When the competition looks at that they justifiably conclude that they need to do the same thing. So in certain niches the SERPs perpetuate a certain kind of low level SEO.
The funny thing about those kinds of SERPs is that the barrier to entry is actually lower than the competition realizes. I have helped clients walk into the top one, two, and three positions for a variety of two word and longer competitive phrases simply with a handful of really good links that trumped the aggressive techniques because we had better relevance and trust on our side. The competition was weaker than it appeared, ranking was easier than anticipated.
3. Now this is the most important distinction about Google SERPs, this is the one that really confuses people because it doesn't fit into the standard SEO box of ranking factors. If you can understand this one thing, then your perception of the SERPs and what is going on will have improved tenfold. Here it is: The SERPs are not a list of the top ten best answers according to link profile.
a. Google does not rank websites in descending order of sites with the most or best backlinks. The site in position three doesn't necessarily have more backlinks than the site in position eight.
b. To further confuse things, there is a random element in the SERPs for the purpose of anticipating different user intent. When someone types Work Accident into the search box, it could have something to with workers compensation law, lawyers, rights, examples, videos, any number of things.
c. There is another random element in the SERPs, and I refer to it as the mom and pop factor
. Google seems to discard what we understand to be the standard ranking elements and throws a site into the SERPs that, based on it's link profile, does not belong there. This circles back to the heart of this understanding about the SERPs: The SERPs are not a list of the top ten best answers according to link profile.