Who exactly told you it is impossible? My chase card lets me generate virtual numbers and use them during online transactions. I always use one when a trial requires a credit card. The number expires in one month and I don't have to worry about any shady billing practices.
Okay, seriously, I spent like 4 hours a couple months ago trying to figure out if I could do this with a Chase card, and failed.
Can you provide URL/directions? I'm not kidding. As far as I could tell, they used to have such a service but didn't anymore; but maybe it's still hidden somewhere but just not advertised, and I couldn't find it?