I think he was referring to Piggy which he did state that he was an ex-British Army officer in the OP.
Ah, okay. Managed to catch the bit of his (Chaz's) background early on initial impression is highly exaggerated. Not helped by Ani interjecting to prompt him with inaccurate shit that pumps his ego. Obviously the guy was not an 11B, you don't IA into a different branch and get a new MOS.
For the rest of it: I'll have to check with a buddy who was on subs but from my understanding of how the Navy handles things physical security falls under the ship's Master at Arms, as he was a missile tech by rate and on a sub, that would be a supplemental duty. I'm sure he got the Navy's quick and dirty shotgun/pistol/rifle training program (I forgot what it's called), but that's not a program that carries any weight. Hell, the Security Forces guys who guard the nukes at King's Bay for three years get no respect when they rotate back to the Fleet.
Now, would the Navy send a missile tech to Iraq? Yes they would, but not how he says. The idea that he went to Iraq to replace a specific solider to cut his deployment from 15 to 6 months is silly. Not how the Individual Augment program worked. This is not my wheelhouse but I have never heard of the Army grabbing people from other branches to assign directly to an infantry unit and I highly doubt it. Given this was the end of his contract, he likely didn't have enough time after his final float to be around for the next scheduled one but enough time the Navy didn't want to let him just chill. What I believe likely was that he got assigned to convoy security to one of the various Naval logistics/Brownwater units in Iraq that would have fallen under the umbrella of an Army Regimental or Brigade Combat Team, as the RCTs were responsible for all units assigned to thier geographic area, regardless of if they're organic.
Okay that probably didn't make sense. Example: One deployment my battalion was going to be in RCT-7's AO, so when we had to go to anything regimental like supply, we would go to 7th Marines' supply or office, despite us being 2nd Marines. We got loaned to a different regiment.
So yeah, I would guess he was doing convoy ops for a Navy unit that was assigned to an Army RCT's AO and is pumping himself up while getting lost in the admittedly confusing web that is CENTCOM's chain of command. Like how he describes the condensed class he went to as School of Infantry instead of ACT. Not saying he's lying, just that's he a submariner and wouldn't be concerned with the difference between SOI and ACT. Maybe my bias but reminds me of the Army MPs who do a tour of convoy ops and declare themselves basically infantry because they saw infantry also doing convoy ops.