NEVER let anyone ever have remote access to any of your machines. If they are legitimate they should be able to guide you through what actions are required to fix any problem, if not they are useless and you should request someone else up the support line.
I usually string these type of callers along for a long time, telling them that I'm doing what they are requesting and giving them gibberish answers. At least this keeps them from phoning someone else and also runs up their phone bill.
There are 10 types of people: those who understand binary and those who don't