If all the above is true, why were they so quick to believe Travis was a pedophile when the DT confronted them with the forged letters?
I don't think they even conceived that a (psuedo).authority figure, Nurmi, would lie to them. So why they may have been quick to "believe" it, I doubt is was resolved in their minds.
The Hughes live in a culture where authority figures are respected and listened to. Their initial reaction to such an accusation would be to believe it, no matter how outlandish it might seem. questioning it would only come after reflection.
People who are thrown into the middle of a horrible murder investigation and who are having the minutae of their lives picked apart get some slack from me.