Sorry to belabor this, but I think it's too important to allow it to slide under the radar, so,
specifically: If you were in the same situation as slolerner's friend
She allowed them access to her desktop, in other words, allowed someone to control her computer from over the phone. (Emphasis added)
and had absolutely no idea what they did, would you feel secure with little more than an anti-malware scan, or would you be fearful that they perhaps installed something malicious that's unrecognizable as malware by a scanner (and, presumably, well hidden, too)?