However, not only is there no correlation between rebates and price growth, but the study also says top brand drugs which offered little to no commercial-sector rebates during the 2011-2016 time period still increased their prices.

Drugmakers also raised prices for drugs that typically have low rebates. For example, drugmakers more than doubled the list prices on multiple sclerosis drugs from 2011 to 2016, despite relatively low rebates on these medications — resulting in an average net price increase of $3,232 per prescription for multiple sclerosis drugs over that time period.

Related: Fault for high-priced drugs lies with drugmakers

In addition to price increases on existing drugs, higher launch prices on new medications have also contributed to rising prescription costs — though these trends are not correlated with drug rebate levels negotiated by PBMs, according to the study.

Among the top 200 brand drugs by 2016 sales, the launch prices for drugs introduced from 2012 to 2016 were double the launch prices for those introduced prior to 2012. While rebates for the second drug introduced into a competitive class are higher than the first drug's rebate 72 percent of the time, the chance of the second drug having a higher launch price than the first drug is only 50 percent.

The authors speculate the true reason why drugmakers are raising prices: Perhaps they are trying to counter shrinking prescription volume for brand drugs. The study provides two graphs showing how brand prescription volume has plummeted from 2011 to 2016 as generics have replaced brands —  at the same time that brand drug prices have skyrocketed to maintain revenues.

Separately, NBC News reports on a Consumer Reports survey which shows at least 28 million Americans have experienced a spike in the cost of their prescription medications in the past 12 months. The price was so high for 4 million of those people that they walked away without their prescription altogether.

"We are nearing a crisis point with what Americans can afford for medication, and it's scary," concludes Consumer Reports. "And honestly, as far as we can tell, there are no brakes on it right now. Congress may have a few things up its sleeve, but we're still waiting."

Lisa Gill of Consumer Reports tells NBC News PBMs are "the middle man" in the equation, negotiating prices with the drug companies and the pharmacies, on behalf of the insurance companies. As such, PBMs are also wrapped up in the blame game for higher prices.

The drug companies blame the PBMs, saying they force them to drive prices up because of all those deals, Gill says. The PBMs blame the drug companies, saying they wouldn't have to make deals if the prices were lower. And, the insurance companies blame both, saying for whatever reason, prices are just too high.

"For the actual retail price of a drug to go down, it would take either government intervention or for the marketplace to actually lower the price," she says.