For the people that have seen nothing, I'm not sure I agree. I think that once they finally declassify a program and its come to light that our government knew all along that they were responsible for certain incidents, then its going to affect public trust in a really negative way.
That's why those projects are being kept as a secret. If they will uncover some secret jet, they will tell them nothing about incidents or testing. Or very little, and 90% of it will be a lie.
Now the consequences... Yes, I think, that there are some consequences. I can give you the same example of school life:
There are those bullies, geeks and middle guys. Bullies are usually bullying geeks, geeks are usually hiding and middle guys are friends with bullies, but are not avoiding geeks. That's the usual story...
So take those middle guys. Most of them are friends with both. They are okay between geeks, but when they come to a company of bullies, when asked outside, they often makes fun of them and doesn't pay attention to what they say. Same with authority figures. They feel ignored everywhere, which makes them concealed. Which makes then just be silent about their opinion.
Imagine a guy, who says his opinion good or bad about a teacher or a bully, getting beaten for his opinion. And then ignored. He feels ignored, he won't say his opinion very often no more. In the long term (let's say 12 years of school), it will probably be his lifestyle. Conceal his thoughts and other things from others, think, that they doesn't care, or he looks stupid. Same with those ufo guys. They have seen something up the sky, they have told somebody, they got laughed at. If the person is not very smart, he could start to think, that everything he says is being laughed at. Or on occasion, other people can for real make fun of him on what he says on other topics, just because he have seen, what others didn't and it's unbelievable. This will make him desperate and concealed, silent.
Those are just my thoughts, most of this stuff is research at my own school, with real people here.