When a Norton product is installed for the first time on a PC it should NOT report a "Secure" system status as there is no guarantee that the system is not infected. For the same reason Norton reports "Attention" when it has not been updated for a few days, it should report "Attention" when the system has never been fully scanned. If I remember correctly, Norton products used to have this behavior (requiring attention before the first scan) some years ago, but for some reason this policy was abandoned.
In my case, I installed Norton on my machine, "Attention" was required only to run the updates, but after that my system status was secure until I found two trojans after a full system scan. I guess this could create a security hole: for example, if someone makes a transaction using his credit card while the system is infected but appears safe, he could get his banking information stolen.