Is what this company did to me fraudulant?

Long story: I signed up for Freecreditreport.com $8.50 per month membership fee. I used my VISA bank card to pay them from my account automatically every month. When I moved upstate, several payees that I used that same card to pay said that their payments were denied. When I spoke to the bank I was told that if they were billing me using the old card information then it would be denied and I had to give them the new address associated with the card. Makes sense right? So I call everyone and give them the new address and as soon as I do they all are able to get money from the old account. Freecreditreport.com sent me an email stating that they were unable to get their monthly payment too but I didn’t call them because I didn’t want their service anymore, so I left it alone. Today I look in my account and see that they took $8.50 from my account. I called them told them to cancel my account and asked how they got my NEW account info. so that they could bill my card. She went to consult a supervisor and came back and the first words out of her mouth were “it was not fraud”. She went on to say that I gave them permission to take money from that account. I told her true but they had been given permission to use had information that was no longer valid and if no one else could get money until I gave them the info. how could you? She repeated her statement, said she would cancel and we hung up. I’m pissed because this doesn’t seem legal. It’s like me giving a fluther friend the keys to my house and telling them they can come in anytime they want. Then I move and don’t tell them where I went but they find me, make a key for the new house and let themselves in stating I gave them permission. I want to call the BBB on these people but first I want some opinions if this is legal.
NOTE: I didn’t OWE them money. The membership fees are paid in advance for the month. If I stop payment they just withhold my ability to see my credit report online until I pay for the next month. I wouldn’t be upset if they took money that was owed to them or for services already rendered.