Wow, problem solved. I thought it was weird when I installed Flash Builder 4.7 and it was still happening. Apparently at some point I set Notepad.exe as the default program to open HTML files and did not realize it.
I feel kind of dumb now but as every other program was working (heck, links even worked in Flash Professional) I was so sure it was a Flash Builder problem.
Anyway, I am just glad to have the mystery solved.