If you play a bit with the configuration under /etc and you accidentally change the permissions of /etc/Networkmanager you can end up with no connection to the internet.
The problem is not too less permissions but too much:
– root with group root must own /etc/Networkmanager/system-connections and have the octal permissions 755
– and root with group root must own the files beyond this directory. But the octal permissions of the files have to be set on 700