geolocation broken on Safari 5 / Windows

Note: this is specifically about Safari 5 on *Windows*. To reproduce:

1. Open Safari 5 on Windows (XP or 7)

2. Go to this URL: http://benwerd.com/lab/geo.php

3. Click "Allow" to share your current location

4. Wait for geolocation info that never appears

There is a separate thread about difficulties enabling geolocation on Safari 5 / Mac. As described in that thread, that problem can usually be fixed through a combination of turning on Wifi, toggling a preference unde System Preferences / Security, and relaunching Safari:

https://discussions.apple.com/thread/2467998?start=0&tstart=0

Those instructions, however, do not fix the issue of enabling geolocation on Safari 5 / Windows. There is no similar operating system preference that can be toggled on Windows, and Safari 5 / Windows doesn't expose any such preference. Is there some secret Windows registry setting to enable it?