I have a Mac OS X Lion 10.7.5. And I'm running on Safari 6. I have been trying to download the FlashPlayer update for the Adobe Flash Player Installer 15 for the past week. When I click on "Install Adobe Flash Player" the download box pops up. It asks for my password, which I enter the box shakes showing that I entered the wrong password. I have changed my password for Adobe and my administrator password. And still nothing. And I cannot uninstall it as I apparently don't have the correct password. I have asked for help on this problem last week. And nobody has been able to help.
You don't need any password to download the Flash Player installer, but you do need your Mac's administrator password to install it.