Yes it is the corps. I don't believe there is a defined area that I know of, but as long as you are not on the dam, or around the picnic area that is operated by the corps then you will be fine. I have never noticed a sign upon entering the marina. Could you tell me where it is located? They cannot ban carry at the marina because the corps has nothing to do with it -- it is entirely operated by the state. If they are banning firearms at the lake (other than the dam area) then a few phone calls need to be made to the Kentucky Parks department.
Perhaps this will help:
http://www.lrh.usace.army.mil/Missions/Recreation/Kentucky/GraysonLake.aspx
As you can see, under "General Information" it plainly states that the marina is not operated by the ACoE. The only parts operated by them are the area that you described, which goes down into the dam area where the picnic shelters and such are.
Here is another page that is probably even more helpful! It plainly says what is controlled by the corps and what isn't with a red marker.
http://corpslakes.usace.army.mil/visitors/projects.cfm?Id=H106790
It seems the two small trails you were speaking of are operated by the ACoE so they are OFF limits with firearms. All of the other trails at the lake are unrestricted though, and carry is allowed.