I think it's because of the pharmacy benefit managers mentioned in the article. You use your card, you pay the negotiated rate that they have with the insurance company. You pay cash, you pay the rate Walmart is willing to sell it at.

Of course it makes no sense that the fiddly details of how you buy medicine matter to the tune of 5x. I guess part of the problem is that an awful lot of people are insulated from the costs of their medical care.