It takes about ten minutes to go over casualty releases to note a number of them who died outside the battle zone, but are duly noted by the DoD. One example here.

We've gone over common sense and the lack thereof in these kind of "theories." How long do you think a bereaved family would go before they noticed their loved one had not shown up listed as a casualty anywhere? Three thousand separate times?

This lie originated, like many others, on the internet, specifically TBRNews. Some nincompoop repeating it on public radio doesn't make it true.

Incidentally, TBR has a "list" of personnel who died but "are not listed as combat deaths." (down at the bottom of the link)

Once again, it doesn't take much research, picking names at random, to find out that the people on this list are indeed listed as non-combat deaths by the DoD. So are 564 others, but they are of course included in the current overall death toll.