You don't get charged for someone leaving a voicemail. You get charged 1 minute of international air time to transfer the call to voicemail. i.e. Someone from the US is roaming in France with their AT&T phone. A call is made from someone in the US it get's transferred to the carrier the person is roaming on in France. The person in France doesn't answer the call and it get forwarded to voicemail, which is located in in the US. Basically, the phone is making a 1 minute call back to the US to transfer that person to voicemail. The carrier in France charges AT&T, which gets passed on to the person's account. That's why you have to turn off voicemail.
My guess is the guy with the Argentinian carrier is probably not having his calls forwarded to voicemail. It might be blocked because he is roaming, because I can't see his carrier eating the cost, when another carrier is initiating the cost.