To further enforce the idea that they know what is happening they get the scamee to do bring up a log that shows hundreds of events on the computer.
Well this is the event log and all computers have thousands of entries so again another safe bet. What they do then is get the client to let them remote onto their computer. The scammers then bang around for awhile on the computer at the end of which they try and convince the
The best response to these guys is to just hang-up the phone. If you have let them onto your computer and you are worried then call your local computer support guy to give your computer a once over.