It was not common for the low-end phones of the type used by Iraqi insurgents in 2003 to be equipped with Bluetooth.
Remember the "NSA can track phones when turned off" was from 2003.
Try to remember 2003, then adjust your memories to match the reality for an impoverished Iraqi.
My guess is that because they controlled the cellular network they pushed out an OTA firmware that made it so the phones didn't actually turn off but went into one of the ARM7TDMI's low power modes where it would wake up periodically and ping a tower before going back to sleep without turning on the screen. Those modes used so little power you wouldn't notice a difference in overall battery life.
This would be trivially detectable by any party with a $10 SDR dongle in 2025.