The exact specifics of computer targeting for any robot in the fallout series is never explained in any game.
It's hardly above any kind of logical reasoning. All the crazy turrets in military bases, your not wearing anykind of ID which we know robots can be programmed to scan for. Turrets in Raven Rock, Eden's assumed direct control to blast his own men.
Rothchild was scathing because they hadn't tested it yet. Dr. Li and himself and only just solved the power problems. The issue was getting Prime to physically work not its programing which If I was Rothchild programing prime to recognize the Brotherhood of Steel as its master would be the first priority before I tried making it functional. Fixing the super weapon BEFORE you program it no to attack you is a really bone head move.
I am perfectly aware of Rothschild's objection, the robot hadn't been tested and prior to that point had never moved an inch; which is exactly why it's so implausible that it would have been programmed to recognise the Enclave as hostiles. It's kind of taken as read that the Brotherhood are programmed as friendlies, otherwise the weapon wouldn't have been able to be tested; that doesn't effect the fact that Lyon's decision to activate Prime took everyone by surprise yet Prime is just able to assume what he's doing, where he's going and what to shoot.
In a real lfie scenario most of the Enclave technology wouldn't work either so its a moot point.
You know what I mean,
walking robots have a pretty large and obvious structural weakness that a trained combat pilot - which we can assume Vertibird pilots are right? - should target. In the opening of Broken Steel three vertibirds just fly past and one purposefully stops in from of Prime to get blown up on purpose. It's stupid.
All three are coming in from behind Prime, they'd blast the [censored] out of his legs and the exposed cabling with rockets and Prime would be done for in seconds. The whole of Take it Back is just a shooting gallery through the streets, so much for the supposedly superior trained Enclave troopers, just be in the road and crouched behind the sandbags.
So far as I can tell the BoS didn't even start fighting the Enclave until after the Oil Rig was destoryed. At which point the BoS was doing the hunting.
They were scouting out Enclave positions in Fallout 2, gathering intel before any more action could be desided upon.