Do not allow anyone to control your computer unless you know exactly who they are and what they are about to do. Do not type in commands into your PC unless you fully know and trust the person issuing the commands. Not only will you save yourself a lot of hassle, and probably preserve your data, but you will not be conned into parting with your money. (You think they are doing it for free?)
Fact: Microsoft is not "monitoring" your computer, and certainly does not randomly call users if they are experiencing problems. If you agree to send error logs to Microsoft, these are collected for statistical reasons, and cannot be used to identify an individual user or machine. They would be in violation of a ton of privacy laws if they did otherwise.
Question: why don't the remote control companies like support.me and ammyy.com have big warning signs on their web pages:
Warning: do not install this software if requested by unknown call centre operators. Only allow remote control from people you know and trust.This would protect many innocent and gullible users and protect the brand of the software. (Update: ammyy.com has done so.)