I once read (I believe it was in the Living the Parshah sefer by R’ Shimon Finkelman) that we need to prevent an appearance of chillul Hashem, even when we do nothing wrong. He gives the following example:
A man is in the grocery store, waiting on line. The line is somewhat long, and he has a full cart. The express lane (10 items or less) next to him is empty, and the cashier there says to him, “I’m empty, even though you have a full cart, come to my register and I’ll check you out.”
The man goes to the lane. A minute later, someone with 2 items comes over, and now has to wait in line for someone with a full cart at the express lane. Did the man do anything wrong? No, he was following the instructions of the employee. However, it creates an appearance of something wrong, and can cause a chillul Hashem, which is wrong. R’ Finkelman suggests that the person should have turned to the guy with 2 items, apologized, and explained what happened, to avoid the chillul Hashem.
Going on the TV show can easily create an appearance of a chillul Hashem. Whether they’re right or wrong, whether they lied or not, doesn’t matter. Going on the show created a chillul Hashem.