Man of Honour
Without knowing for definite I'd hazard a guess that they'd simply be seconded rather than getting paid twice i.e. you lads are reporting to this company for the duration of the Olympics, you do what they tell you and you'll get your normal wages as normal (maybe plus overtime if that exists in the armed forces now?).
It works out cheaper overall than employing private security firms and there isn't an issue with getting enough security personnel that are trained to a sufficient degree if you're employing the armed forces to provide the cover - they're already trained above and beyond what is needed.
That does make more sense, and the private security firm that has been contracted to the Olympics minimises it's overheads - though ultimately we're still paying for it