You are right. He did not say this. He was a big believer in a dark side of human nature, one that is selfish, egotistical, and just fundamentally bad. However, he was also a proponent of republican government (as opposed to monarchy or dictatorship), believing it was the best form of government, even if imperfect. The "psychology shows statement" comes from me, and is based on some particular studies that showed how humans, despite all the negative selfish traits they have and their dark side, do come together sometime. That's why I wrote "in a roundabout way" in the closing statement. While Machiavelli was all about the evil side of humanity, he did acknowledge the light side from time to time as well. He was above all a pragmatist.
I also wrote on the dark side of human nature. Despite the propensity of darkness (in line with Machiavelli), there are some things which do overcome this.
This is the quote from a scientific experiment that I was referencing:
"It is important to reiterate, however, that the intergroup landscape is not unilaterally bleak; group membership alone is not sufficient to elicit intergroup empathy bias. When group members are engaged in a cooperative task with an out-group or receive cues that diminish perceptions of group entitativity in a competitive context, intergroup empathy bias is significantly diminished. Better understanding on how to change malevolent affective reactions with small, unobtrusive interventions in a controlled group setting may give us insights into intervention design for real-world intergroup conflicts."
from this study: https://www.sciencedirect.com/science/article/abs/pii/S002210311400095X
