I thought it was caused by poor design of the website, where they could've used the Z-Index property in Cascading Style Sheets.
According to this page, z-index wouldn't even solve it, and the problem was actually caused by Flash Player 9 on Linux (only).
I grabbed a copy of Flash Player 10 and installed it, and now everything works as it should!
I run Kubuntu 8.04 and installed the package manually. Download the ".deb" package then run this command:
sudo dpkg --install install_flash_player_10_linux.deb
After the installation is over, restart firefox and the new flash player will be loaded.