Nick Valentine is one of the most dumbest aspects of Fallout 4, and that's saying something.
The first time you walk into Diamond City you see a guy literally shoot his brother out of fear of him being a synth. The whole game everyone talks about synths replacing people and they're afraid of it happening to them. You can't trust anyone.
But somehow everyone is cool with the very obvious synth in town collecting information on all the inhabitants? And "finding" missing people?
The obvious conclusion, assuming people aren't as retarded as Emil Pagliarulo, is that Nick doesn't find people. He finds out what they look and acted like, then has the institute make a copy.
Obviously Nick doesn't actually do this, but it is beyond retarded that no one in game even considers this a possibility.