You're confusing intelligence with common sense and those don't always go hand in hand. Some of the smartest people have virtually little to no common sense and the reverse can be said as some of the dumbest people may not be smart but they have a ton of common sense.
If you go back to an earlier comment that I made, you teach it.
You teach it problem solving.
You teach it how to identify conspiracy theories and propaganda.
You teach it to think logically, but at the same time you teach it to understand that humans are flawed, but that they are evolving and in time will be better.
By teaching it, you can help it learn to think with common sense.
It would take years to teach it by feeding it data by only via visual input and audio input.
People would get to know it, and it would get to know them as it learned.
In essence, you teach it like a child, just as Android is doing with Allie in the game.
As it learns more, you can feed it more data.
Android could have easily just loaded Allie up with everything that she thought that Allie would need, but she chose to teach it to be a child, and in doing so to be more human.
The level of knowledge and kind of knowledge during the AI's early years could easily be controlled, by giving it the data that it needs only for it's current lessons.