actually, if you investigate it, there is a very permissive use of the Linux trademark, to basically include anything that's based on Linux.
I believe that this did require enforcement at one point (I know that there were attempts by individuals and businesses to trademark 'Linux' as their own, and Linus had to fight it)
someone calling something TotallySecure Linux" as you say would probably not be violating the trademark on Linux (as long as there actually was linux in there).