Well... I found the problem. Oddly enough, IE and Mozilla see relative documents differently.
IE was working and considering the current directory for the SWF the one where the HTML file that loads it is, while Mozilla considers the current directory the one where the SWF file is regardless of where that SWF file is embedded.
Threw an IO Error in Mozilla but also a HTTPStatusEvent, that is why I tried to move the uploading PHP and see if it works.
Strange.