I would treat this claim with a great deal of skepticism. However, this is by far the smartest play for the government. Had they gone to court and lost (probably after an appeal), they would have set a precedent that would be very problematic for them going forward. By claiming this, falsely or otherwise, they hurt Apple's security reputation (most consumers will not understand or care that this happens to be an old iPhone with an old version of iOS - they will just hear or read that an iPhone was cracked), and they avoided a potentially problematic legal outcome.
The DOJ came out on top here, whether they are lying or not.
The DOJ came out on top here, whether they are lying or not.