That might be because it's the same controllers in the same control centers that control GAT and OAT traffic (When OAT is flying outside TSA's)
OAT is transparent to us controllers FPL wise, the SSR code assignment for ATO traffic is the only difference.
It's just ARR/DEP aerodrome + relevant ATCC(s) (3 in total)
The rest is transparent to the outside.
My point was more that it's impossible (correct me if I'm wrong) to file GAT IFR over a MIL owned/operated navaid via CFMU in the UK. The C130 flight I mentioned was a trash hauler GAT flight, but as soon as we tried to leave the Civ route system the CFMU reported "unknown navaid" if I recall correctly.
Problem solved when we slipped a "OAT" into field 15 at the point the route left the CIV routes.
In Germany MIL navaids are "CFMU compatible, as is the case in scandinavia.