I am total newbie and only need an advice on the existing payment processing services available.

So far I have checked only Bitpay, and noticed that on its t&c it is said that the system converts bitcoins into fiat once they are received. I guess that means that the client has to be able to pay by bitcoin, and I find it can be an deterrent when dealing with payers which are not used with this new currency or are unable to pay with them.

So the question is: are there 'blackbox' services, which allow the payer to send money to the payment processing system by using fiat money, effectively allowing both users (payer and receiver) to avoid 'handling' bitcoins directly?

Thank you so much