Well, if you do have Quicktime 7.1.2 installed, something is preventing F4M's installer script from seeing it. Since that "something" isn't being cured by a new user setup, the problem must be in your system files, somewhere.
You might want to check /Library/Receipts and see if "Quicktime712.pkg" is present, or for that matter, any version of Quicktime present in that folder. Also check /Library/Internet Plug-ins and see if "QuickTimeplugin.plugin" and "QuickTimeplugin.webplugin" are there and both are at version 7.1.2
If there are any plugins installed by VLC, remove those to the desktop. VLC's plugins have been reported as being very problematical, so if they are present, best to get them out of the picture. And just to be sure, /Library refers to the Library folder at the root level of your hard drive (accessible by double clicking the Macintosh HD icon on your desktop), not the Library folder inside your home folder
Third, fire up Safari, go to the help menu and select "Installed Plugins." Verify that Safari is reporting the presence of the Quicktime plugs and that the version is correct.
If all of that checks out okay, then it's a mystery to me why F4M's installer is reporting an improper installation of Quicktime, You could try - sigh - repairing permissions, but I wouldn't expect very much from that.