The permissions verification results is not related to the OP's display sleep problem. It can be ignored. It is not a problem to be fixed by users. The permissions on the folder is expected. The folder is supposed to owned by user/group _displaypolicyd (244). Changing the permissions can cause problems by not allowing the displaypolicyd process from accessing the folder. The permission verification results is due to the Mac OS X OS package initially creating the folder with different permissions. I've included technical information below from my mac.
The system process that needs access to the folder:
USER PID %CPU %MEM VSZ RSS TT STAT STARTED TIME COMMAND
_displaypolicyd 58 0.0 0.0 2560836 2888 ?? Ss 1:14AM 0:00.41 /usr/libexec/displaypolicyd -E 1 -k 1
The runtime files that the process creates and needs to access:
drwxr-xr-x 4 _displaypolicyd _displaypolicyd 136 Dec 28 13:21 /private/var/db/displaypolicyd
-rw-r--r-- 1 _displaypolicyd _displaypolicyd 4 Dec 28 01:14 /private/var/db/displaypolicyd/.pid
-rwx------ 1 _displaypolicyd _displaypolicyd 4276 Dec 28 13:21 /private/var/db/displaypolicyd/displaypolicyd.cache
The file information from the installer package receipt that is used to verify and repair permissions:
volume: /
path: /private/var/db/displaypolicyd
pkgid: com.apple.pkg.BaseSystemBinaries
pkg-version: 10.10.0.1.1.1412852630
install-time: 1413835468
uid: 0
gid: 0
mode: 755
pkgid: com.apple.pkg.BaseSystemResources
pkg-version: 10.10.0.1.1.1412852630
install-time: 1413835469
uid: 0
gid: 0
mode: 755