It's not from the internet, your not getting a prompt to download something, therefore it's already on your computer. Unless you screwed with your settings, firefox will tell you are downloading something and windows xp and onward by default asks permission to download everything.

by your description it is not false positive, you have a virus of some sort

I still say scan the heck out of your computer, if it doesn't fix it, reinstall the operating system. if you don't want to deal with these issues again and don't rely to heavily on pure windows programs look into this.... http://www.ubuntu.com/