I would say that if the site receives traffic, it could mean it has some (or a lot of) authority. The way I see, if the site has got things like videos, social posts, forum posting (with sig links), blog comments (for traffic, of course), etc ... all of those certainly affect the SEO and rankings, not necessary traffic volume by itself.
If traffic volume was one of the ranking factors, I could easily by expired taffic from providers either here or on 5rr and rank the hell out of my sites ... unfortunately, this is not the case ...