True narcissists are very good at covering up how shitty they are in the public eye. They use either Te or Fe (or a mixture of both) to manipulate things in an external way to look like a 'good person' but interpersonally they are shit. Society as a machine doesn't care so much how genuine or 'real' your compassion/morality/empathy is as long as you can have the right veneer that you are this way.

Type wise I don't see ILI as likely to do this much at all. More like the opposite. They are probably more likely to look like jerks on the outside but treat their SO like gold. An ILI that's unhealthy or sadistic is very obvious though.