SA can be regional, varied in it's inaccuracy and is done from the transmitter (satellite) end. Furthermore, GPS jammers are commercially available and probably in use in Iraq due to the Coalition use of GPS guided munitions. GPS signals are easy to jam due to the very low transmitter power and the long time needed to transmit the time signal which the receiver uses to calculate it's position.
The military signals use a different frequency to the one your Garmin receives and can also use encryption to negate the effects of jamming.
I flew 40 miles North of the Iraq border yesterday and our FMCs were still happy to use GPS updating over DME/DME and raw IRS data - showing an ANP of 0.08NM.
A handheld GPS in the back of an airliner is going to fairly unreliable for lots of reasons.