I'm having a very similar experience. It is a nightmare! 

In January, our new CFO (the finance director had left the company) moved us from desktop to QB Online. Intuit staff helped with the transition (obviously) and we thought we were done. 

Then my credit card was charged $3,700 in July for the desktop product that we stopped using in January. I have been on 9 calls and have submitted a request to become primary admin for the desktop service FOUR times. Each time it is approved, but Intuit changes the Online account, not the desktop. And when I try to speak to a supervisor in customer service, they won't let me because I'm not the primary admin. THAT'S WHY I NEED TO SPEAK TO A SUPERVISOR! I'm giving it one more day to see if I get a response, then I'm going to file a complaint with the Better Business Bureau. This is ridiculous. And a nightmare.