My understanding is that when you install iOS on an iPhone, an Apple server signs the OS as part of a challenge-response protocol. The challenge includes a unique device ID, and I believe the signed iOS is only installable on a device with that ID. http://www.saurik.com/id/12 has more details.

Think about this in the context of jailbreaking to understand why such a facility exists. Apple doesn't want users to install their own modifications to iOS, and they also don't want users to install old versions of iOS that have vulnerabilities that would allow people to modify the OS.

One way you could implement something like this is to have a public/private keypair within the device and have updates encrypted with the public key; then design the device to only run an OS that it could decrypt with its private key. To do this well, you would need a TPM that did not allow the private key to leave the device, nor to be reset.

All iOS software updates, even the normal ones, bear a digital signature that incorporates the device's UDID. The bulk of the software update is the same for all devices, but Apple must generate a new signature for each device using Apple's private signing key.

I don't know if Apple has any specific capability as part of the firmware verification, but even if they didn't they could just put something like this early in the boot process:

    if (unique_device_id != SAN_BERNARDINO_DEVICE_ID) {
        halt();
    }

If this code must be signed to execute then it can't be modified to work on another device without Apple signing it again.

This assumes there's a unique device ID that is known to the FBI and can't be tampered with. Maybe the serial number or IMEI?

Fixed that for you:

    if (unique_device_id != SAN_BERNARDINO_DEVICE_ID) {
        goto fail
    }

My understanding is that phone thieves routinely change the IMEI by desoldering and replacing a chip. If this weren't the case, I think it would be fairly easy for detectives to call up the person currently in possession of any given stolen iPhone.

Maybe ECID then? https://www.theiphonewiki.com/wiki/ECID

It looks like there's something called a UDID which is a SHA-1 hash of a bunch of identifying information. So, difficult to fake even if you can twiddle the source values or swap in new chips.

https://www.theiphonewiki.com/wiki/UDID

Except they have the shooter's phone, which has the identifying information which results in the correct UDID. To get the same UDID on another phone they just need to change the source values to the same values as in the shooter's phone. The fact that it's a cryptographic hash doesn't really help here, assuming they can change all the source values at will.