That trust should not rely on people having to censure themselves all the time, since that would be harmful for an organization's performance in the long run. And a lot comes down to how that criticism is delivered.
It's like a skill we take for granted. When you see people with certain mental disabilities who can't regulate their words, it quickly makes you realize why self-censorship matters. It's a critical tool for keeping things from descending into chaos.
The question isn't whether self-censorship is necessary, but rather, how much is appropriate. I shared the example of someone who revealed a boss's affair during a team meeting. It was a moment of impulsiveness that led to serious career consequences, to put it mildly.
That ability goes out the window once all communication is written down verbatim because now people can point fingers and have a grudge with each others for years.
Now, that affair with the receptionist is really HR's problem, and it's just great for one's prospects at the company to inconsiderately flame on the boss' way of doing things (not!). But somehow it should be possible to criticize things without having to join management at the golf club or at pub crawl...