Installed it yesterday and yes, normally you do need the download manager.
This should not be the case. But here is a workaround.
Download the Flash player installer 10.1 using IE browser.
Save to drive, then run the Flash Uninstaller, now run the new 10.1 installer.
Check it in IE and Opera
http://www.adobe.com/software/flash/about/
You will see version 10.1 is installed. Now run the check in Firefox.
It will not run and prompt you to install a plug in. Do it and now it say
Flash 10.1 is installed. No download manger.