People distrust "we're a family" because it's an illusion, not because of the potential for an actual sort of "family" or friendship. But they may also come to distrust "we're not a family" once it becomes as cliche and they realize that every company they work for that makes such a claim will inevitably devolve into making the employee-employer relationship out to be more than it actually is or should be.

I disbelieve most corporate values because companies are run by humans, and humans are pretty bad at self evaluation. Well, that and I've had enough experience to tell me that explicitly stated corporate values usually mean very little in practice. Only you can unveil a company's values, though that's no easy task beyond some basic red/green flags.

Of course I am assuming those that use said mantra are refering to the touchy feely version of family and we are not going down the 'what does family mean anyway' rabbit hole, where rivalry even Fratricide and Parricide, they even have a word for killing a family member.