The people needed someone to believe in after Iron Man's death and most of the other heroes seemingly going AWOL. Mysterio filled that void and gave hope to those who needed it. Taking that hope and smashing it to pieces by revealing what happened is only going to make things worse and perhaps turn the people on themselves. Therefore, I would speculate they didn't reveal it initially because it was in the people's best interests.
Now though that Mysterio played his one last trick and made Spider-Man look like the bad guy and revealed his identity, they might explain what was going on and that Mysterio was the bad guy. However, as that was only shown in the post-credits scene and we don't have any future works, yet we will have to wait and see.
Also, the fact that Fury was off-world and Talos was impersonating him probably plays some part in it as Talos presumably has to get orders from Fury to act like that as we saw when he "calls" him up.