Ok so I got to the bottom of it. Aparently this did have to do with the site being set up as a local business.
Google did not have support for social icons for the "local knowledge graph" until the 28th/29th of this month (July 2016). Up until that time it only supported large/well recognized brands and companies and that wasn't even always the case until earlier this year. Ironically after having the site up for about two years I decide to ask this question days before they implement it.
I talked to a friend who works at Google and he verified that this was just recently implemented. There's also a twitter discussion about it here.
Google will find and implement the links on it's own if the social profiles have enough authority. But you should also use the Organizational schema markup on your own site.
"legalName" : "Disputebills.com",
"contactType": "customer service"
It's also important that you're an owner of the google my business page as this allows you to edit the social links google adds on it's own (even though you can't remove or add them you can edit the ones that show up). Your site needs to be activated in the google search console / webmaster tols so it's connected to your website.
I'd also throw in the facebook meta tags, twitter, metas, and any others that you plan on using, and even the publisher tag
<link rel="publisher" href="https://plus.google.com/103378801284776045769">
and make sure you actually have clickable links, and maybe even some share buttons somewhere on your actual site to have a better chance of getting them to show.
To be honest I'm not convinced that the schema markup has nearly as much impact as having credible social profiles (ones that actually post frequently, have links to them, from them, and have followers. The example above "dispute bills" is a good example. You'll notice that google plus isn't currently showing up because we don't really use it all that often and barely have any followers where the other ones we have a lot more. I noticed this trend across all the sites I'm hosting.
If you have done all of the above re-crawl/index your website in the search console and report an error/feedback to google about the your business knowledge graph.
Anyway, I suggest checking out Jane's twitter discussion on this as well as the rest of her twitter posts as she seems to be very on top of the latest "Google Local Business" trends.