A good deal of denial, I think. No one wants to be that crazy person in the tabloids. It's easier to accept what your eyes are telling you and not just make up excuses when you have someone else confirming that you just seeing things. Before we knew that demigods existed, B- Bianca and I saw plenty glimpses through the Mist, but we would brush them off because, well, it wasn't possible that those things existed.
More horrifying in that they look harmless. Just some swaybacked, fuzzy cows with their noses to the ground, but then they look up and bam. I hear they put up a good fight too.