Greg,
Here's the background on why 777 would even be a reasonable idea to begin with
There are 4 directories within TYPO3 (fileadmin, typo3conf, typo3temp, and uploads) that need to be set up to allow write access from the web server. Depending on the server environment, Apache might be running as www, apache, nobody or as your username. If you've got root access to the server and technical expertise to know what user Apache is running as, then your best bet is to keep world privileges completely off and lock things down to the user and group that Apache is running under.
Most people in a typical shared hosting environment don't have the ability to tweak the permissions in this way, so running everything with full world permissions (777) ends up being the best option. In these environments, access is limited to the home directory of the current user so world permissions aren't quite as scary as they'd normally be.
Hope that explains some of our logic in recommending 777. Rather than being the best option 100% time, its a compromise to come up with a recommendation that will work for the vast majority of our users.