Its actually not a terrible idea.
Online bill payment via Bitcoin would be a perfect fit. You don't need instant confirmation, an hour or two would be totally acceptable for this purpose.
Taking BTC may save both users and the company on transaction fees associated with credit card payments etc.
Though if they use fiat currency then that would mean it is stable and they would be trusting the fiat currency to remain the same. However, for example, if an insurance company tries to use bitcoins then that would mean they are relying on something unstable and the price is volatile. What if bitcoins crash? That would mean the insurance company will also crash, bye services.