I think it's the latter. On a couple of the ones I've received I first speak to one of the call staff, then I get transferred to a techy, then I get transferred to someone for payment. It obviously works, so why would they be a team of a couple of people - they must have plenty of staff ringing...
I get a lot of these calls about my PC sending error reports etc, and I think they all ask for me by name. I assume there are several similar companies running the scam, as the calls don't stop.
People need to be educated about scammers, loads of people must fall for it.