To be honest, it's not even about covering my trail. I used my real info when setting up the prepaid card. It's more about making sure that if the card info gets swiped (a real common occurrence with international card processors, especially at the pharmacies it seems) I don't want them to get any money or deal with the hassle of dealing with the credit company to get it all sorted out. This way, I put exactly what my pharmacy order costs plus $3 (what the card charges you a month), place my order, and then I'm done. Once I've sent the money to the pharmacy there is nothing for anyone to steal.
I've met enough people that have had their credit info stolen to just not want to take the chance. I have noticed an attempted tiny charge on my prepaid card (something ridiculous like $0.84, likely done as a test charge on stolen cards) so I don't fuck around with real cards internationally.