Someone I know has an account with one of these firms that offer cheap international calls by prepending a prefix to the number you dial. Frustrated that he couldn't register his work number with them to use it, he tried changing the caller ID his work phone issued to make it appear as if it came from his mobile, and lo, it worked - he could make international calls on his account. (His workplace is something telcoms related, and is set up to be able to change outgoing caller ID for legitimate work reasons)
Which, of course means that he could just as easily make international calls billed to anyone else's account, if he knows which phone numbers they have registered.
So, all that remains is to set up a premium rate phone service abroad, and let the scamming begin.
Please note, this scheme may not be legal. :-) But it's certainly do-able, which is worrying. Authenticating on caller ID - bad plan.
I wrote IVR code to do precisely this.. authenticate and login to an account using caller-id (they call it ANI, authorized number identification).
It was even easier in my case.. Large companies basically give you a list of numbers and say "look, if anyone calls come from these numbers, let them through without authentication" (I asked everyone several variants of 'are you REALLY sure you want to do this'? but they still wanted it).. Find out the director's office number, change your caller-ID to respond with that particular number on request and you're able to do VOIP calls to anywhere on the planet. And it would certainly take a while before you get detected.