Either of your explanations of negligence on Getty's behalf could be correct. IMO neither should mean they avoid the full charge for infringement/false attribution/fraud (whatever) for the attempt to sue people for using works Getty had no rights over.
Yes, it's fine they might have had a computer glitch that mislabelled things, yes they may have bought a batch of images with dodgy copyright/origin information.
But, at the point at which they instructed personnel to issue a demand notice for infringement there is no excuse for not first checking they actually owned the rights to the images in question. The deliberate avoidance of checking their rights prior to their negligent infringement demand - for a company whose raison d'etre is handling copyright and licensing of image - is well beyond the bounds of criminality. Ignoring the information presented to then that they were acting tortuously, makes for reckless infringement (at best) on a massive scale and should really be leading to personal criminal prosecutions for those who oversaw (or neglected to properly oversee) the creation of such systems.
The relevant investigatory powers should be inside Getty now looking to see if there is evidence that this was a known commercial practice of Getty to fraudulently misrepresent their ownership of other's copyright.