This is a tryout on how androids could be logically explained. There will be plotholes in this, like, why didn't the institute behave otherwise, but those I neglect, because it's a tryout.
The institute (which has become more than researchers in a sheltered bunker) had dominated most of massachusetts in the first 100 Years after the Great War. As a corporation leading an entire state, they enforced law in the wasteland, contributed food, water, weapons, technology. But they also contributed forbiddance of these weapons, and rationizing of water, and forbiddance of speaking their name in vain. Those who opposed them were silenced or even brutally tortured right on display of the local inhabitants. The institude hadn't really expected what would happen to them in the near future. The outer countreyside was the first to fall to the maroding hordes of revolutionists, leading an assault to the heart of their government, the MIT.
The institute were taken by surprise, as parts their own army revolted against them, to enforce the law of the people over their government. Robots and superior weapon technology cost many revolutionists their lives, but those were considered martyrs, and the revolutionists saw themselves at the winning side, because their ever increasing numbers simply dwarfed those of the institue. So if the institute wouldn't be able to do anything this would be their demise. And it came to their genius minds what they could do. Giving up, saving their hides? No chance. Winning Power back again. Enforcing their law. Wiping the slate clean. Equalize the battlefields.
Yeah, the Institute are really bad guys. Or at least were. Like the church.
After the second launch of nuclear warheads on the New England Commonwealth, things didn't look too well for humanity there. They soon populated the land again, yeah they were good at reproducing. But many of them had turned to ghouls, feral ghouls, ghouls, feral ghouls, ghouls, feral ghouls. Civilization fell back in to a state of tribal organization. Many a tribe worshipped the ghouls, many a tribe burned the ghouls alive, many a tribe simply didn't give a [censored]. Over time, the tribes established connections and came in contact with merchants, slaves and slavers and missionaries from southwest, strengthening their relations and organization, while modernizing their standards of life and therefore their culture.
The institute worked secretely inside the vault-like sheltered interior of the MIT. Somehow they came to an agreement of how the situation could be handeled in their favor. Creating a new way of thinking. Helping the tribes understand the true way of thinking, of understanding that the institute were the good guys. Unfortunately many believed the MIT to be the Maw of hell after the Second Nuke.
So they created androids. These would infiltrate the tribes. Immune to radiation and provided with abilities beneath the human body, they resemble superhumans or mythical creatures like angels or demons to the locals, they were worshipped by many, because they resembled humans in every way, but had skills like a saint. Their wounds healed extremely fast. They had insane medical abilities. Their Wired Reflexes weren't constrained by the human body. But they didn't worship no god, but the institute, that many associated with evil. So many of those who didn't worship the androids, burned them alive.
To be continued...