Many fact checking sites are actually heavily opinionated. To the point where even demonstrably true facts are labeled as "half-true" due to opinionated objections. Frequently, the veneer of calling oneself a "fact-checking" site lets them get away with some pretty significant bending of the truth.
It looks like this article isn't much different. It doesn't actually refute the claim that less regulation would result in lower healthcare premiums:
> In states with unregulated markets, “you could create a situation where you are selling very low-priced policies to healthy people without much [insurance] protection whatsoever,” Blumberg, who was a health policy adviser to President Bill Clinton’s administration, said in a phone interview. “But that ignores the fact that … what you’re doing is driving up the premiums to impossible levels” in states that want to have insurance regulations.
So removal of regulations would actually make healthcare premiums cheaper in the de-regulated areas. Potentially this makes the insurance more expensive in places that do have regulations, but it's actually agreeing with the claim that deregulation can make insurance cheaper.
> It’s a “risk-segmentation strategy,” she said, where eventually the healthy people are pulled into one set of plans and those with health problems are left in another. Premiums would go up so much in states with regulated plans that it would become impossible for them to sustain those regulations.
> Sabrina Corlette, a research professor at Georgetown University’s Center on Health Insurance Reforms, said that the lion’s share of a premium is the money a plan has to pay for medical claims, as well as utilization. Selling insurance across state lines wouldn’t change the price of medical services — as Antos said — but if insurance companies could deny coverage or charge more for health conditions, a carrier could “push down on utilization by screening out sick people” and then, “they can charge a lower premium.”
Again, the article does admit that premiums would likely go down with less regulation.
It looks like your article isn't actually disproving the claim that insurance premiums would go down with less regulation. In fact it repeatedly does say that premiums would indeed go down, but that it would result in other changes like different coverage from what people are used to, and potentially making it harder for unhealthy people to get insurance.