I would like to add that I successfully reproduced that behavior with another fresh install of wordpress 3.5. Additionally, I tested installing UAM on a wordpress 3.4.1 installation, then switched file locking on, then upgraded to wordpress 3.5 and it's working. But this is of course not a solution for the site I am right now building, as this would mean to begin from zero again.
I also found out that the settings for "file lock" looks different in the installation which has been upgraded: there is two options: "Locked File types" and ".htaccess password" which don't appear on the not working version. See http://christiananton.de/stuff/wp_uam_working.png and http://christiananton.de/stuff/wp_uam_not_working.png.
In my "not working" installation where I have installed UAM on a freshly installed WP 3.5 I also found out that the links used for previews/thumbnails for images doesn't contain the "?uamfiletype=attachment&uamgetfile" part which makes uam giving access to the files, the internal URLs used are still direct links and therefore no image previews, thumbnails etc are visible.
It seems that these two things have something to do with each other, maybe some mechanism in WP has changed so that UAM cannot successfully install all its components...
So, I really hope this get solved soon.