Certainly in the case of a credit card number, it's assumed that what you will be reading off is all numerals so there's no ambiguity nor is there any other digit for which the oh might be confused. In that context I would worry more about five and nine being confused.

I did once fluster one of these new voice recognition programs that was helping me order a telephone book by pronouncing 3 as thu-ree. By the time it had found itself back to some sort of order it had decided that my request for one phonebook was really a request for 236 phonebooks. It took me a bit to doing to disabuse it.

Still waiting for the phone police to come knocking at my door at 3 in the morning to arrest me for telephone disabuse