I think we're ultimately better served by the latter approach.
Four planes were hi-jacked. Three of those did not know that the outcome was to crash the plane into a building. But one did, and (as far as we know) the people aboard prevented that.
If the American people would simply have been informed that terrorists didn't want to steal planes, but instead fly them into target then 9/11 would have turned out very differently. And we know this because we have proof.
The solution to this threat was dispelling the notion "getting hijacked means a short vacation to Cuba" and replacing it with "getting hijacked means that I get to kick a terrorist's face in".
This solution was implemented and successfully tested on the morning of 9/11/2001.