This is 100% a scam. This person was not working for Microsoft and Microsoft would never call you for no reason.
This is what is known as "phone phishing" it is can be a very serious problem if you do let them access your computer.
Basically what they will do is call a lot of phone numbers and say that you have problems. Any actual computer problems you have will be entirely coincidental. Usually what they will do is show you the windows error log which always shows a lot of errors but these are normal and on all windows computers, they are not viruses.
Next they log onto your computer and lie to you about the numerous problems they pretend to find. Next they will attempt to get you to pay a few hundred dollars to "fix" the issues when in fact they actually do nothing.
Sometimes they lock people out of their systems and steal their credit cards as well.
Here is what Microsoft says on the subject:
Always remember, no legitimate tech support company would ever call you. Your computer does not report to Microsoft or any other company so if any tech support person calls you can trust it is a scam and just hang up.
Give yourself a pat on the back for this one and questioning if it was legit. I have helped many others who have been taken in by this scam and once they let them on the computer it is too late and the damage is done.
If you need further help please do not hesitate to reply back and let me know.