remote support

Recently I had problems with my Internet Security.  I ended up having remote support.  While the technician was in control of my computer, I noticed him going places I didn't think he should be going, such as another computer on my network.  He eventually fixed my problem, but this weekend my facebook account was hacked from somewhere in the far east.  The technician that was on my computer had a name that I would associate with that region.  So, without actually accusing anyone, is there a way someone could get my facebook info just by being on my computer?