Staff fudge the truth to bosses all the time. The issue doesn’t lie with the staff because it is the boss’ responsibility to understand the power disparity and do their best to mitigate it.
The way to do that is have a small contingent of 2-3 people who will ALWAYS tell the truth to the boss no matter what.
But again, that willingness to hear the truth and have those people around starts with the boss. And if they just want yes men around, that’s what will happen.