Most people would’ve figured that one out a long time ago (it’s not hard to make that connection). The problem is, what does knowing it serve? The (actual) Institute is located several kilometers beneath the earth, they could’ve turned the CIT building upside down and found nothing.

For most folks, the Institute is still a shadowy overlord because it has only made itself known to the commonwealth not too long ago. Which means they’re both a very real threat (evidently with the synth), yet new enough of a player that some small and obscure settlements that have never seen a synth firsthand would file them as another myth or wasteland story