A couple things to note here, in my opinion: Of course, links that get clicked represent quantifiable signals of user interest/intent. Google should (and probably does) certainly consider that click as a signal the backlink is more contextually relevant, thus, it probably will provide stronger "juice", traffic (obviously, right?), rank potential, et al. I just saw this within the last 24 hours, with a press release I wrote and published/syndicated. I had massive click-through from the story (real-time traffic on G Analytics at 8:00 in the morning, when we're usually slow, was up by a factor of 8 to 11), and when I checked the SERPs, the article grabbed the #1 result for that query. Guess I got lucky and pub'd on the story before any news sites or competitors did.
That said, here's my very tangible and recent take on backlinks overall, with a pretty good example: I've started managing a few eComm sites in a very well-defined, specific widget niche. The sites I manage have well-established traffic, they rank top 5 or at least page 1 for their target keyphrases at almost all times, and SEO best practices are adhered to. Consider these sites "healthy", regular ole' sites that dominate (or almost) their market.
I've contributed very many backlinks to these sites in an effort to pump up one of the two sites that likes to bounce between spots 5-12. In SEO, we often talk about getting a single, high-DR backlink from a relevant, authoritative place as impactful, noteworthy, beneficial. I can tell you I've secured comparatively large amounts of credible, relevant backlinks on decent DR (35-45) and high/very high (77-94) sites with guest posts and syndicated content. With volatility, the crazy SERPs since about June, and all the algo updates/smaller updates, I can say, unfortunately, it appears none of these links have helped much! I pruned a lot of bad blog posts and content that performed poorly, or received no traffic. I saw a consistent climb in rankings and traffic, then the last round of wizardry from Google came 'round, and it knocked everything loose.
TL;DR: Basically, my sites' backlink profiles are *way* better than my competitors. I've added many high-DR links in a few months. They appear to have been unable to insulate the sites from volatility, poor SERP performance with no apparent reason or clear indicators that it is justified, etc. Even with optimization and SEO best practices otherwise helping performance improve quite a lot... Before the usual turmoil.