The w3tc version on GitHub is a community-driven fork of the official w3tc.
It contains fixes to bugs commonly reported by users, but is not officially maintained by the w3tc folks — the patches are from a bunch of volunteers.
That being said, several of the patches committed to GitHub actually end up being adopted by the official w3tc team and make their way to the w3tc version hosted on wp.org.
The fix for the bug in my first reply (here) has been accepted by w3tc team, and will be available in the next plugin update (whenever that comes).
So, if you want to try it out before the plugin release and see if it fixes this problem, you should apply these changes
Basically, in ObjectCache_WpObjectCache_Regular.php, in function function get look for $this->cache[$key] = $value; and move it inside the if ( $value !== false ) block.