I've never seen a completed call not get captured in the billing statement.. The only thing I can think of is it might be possible to "call forward" calls to another phone and not have them show on the bill, but I don't know if that would be the case. I've never tried it.
Actually it is pretty easy. Sign up for a Google Voice account. Then make outbound calls using the service. That doesn't even count the number of services that offer VoIP.
Not trying to make you paranoid hoosjim but with modern technology it is too easy to conceal who you are talking too.
