This is the same reason I pay bills via my bank bill pay rather than giving EFT access to the folks who send me bills. One point of control, and the bank is invented to help me with payment issues rather than throw up roadblocks.
Yeah, it's not all peachy there either. I made the same assumption till I went to the bank to "block" a service-provider that kept insisting on billing me. They "blocked" the service-provider from charging me for 3 months, then they were apparently obligated to let it through because they could only do it for 3 months. At which point, the service-provider just back-charged me for those three months and continued anyways.