The family's immediate reaction was caught in the episode's sneak peak released by The Wrap.
"Joe we are blue, all things considered," Brown said in a phone conversation with Joe Darger, a fellow Mormon practicing polygamy.
"It's so disappointing not being able to have justice heard," Darger could be heard saying on the speaker phone."
"There's silver lining in our loss. That means the gloves are off for us if we want to fight," Brown responded.
The conversation ended with Brown wishing Darger well in "fighting the good fight."
"It's like a live and let live country, or (it's) supposed to be," Brown said. "Why are polygamists still marginalized? Because one segment of polygamy has a sexual abuse problem? Well then prosecute the sexual abuse then! Leave me out of it!"
"They're always looking down their noses at the polygamists. We're always small, little people to them," he continued. "I am aching in my heart for my freedom. I am aching for my liberty. ... We're not all pedophiles and perverts and abusers and welfare frauds."
The federal case, Brown v. Buhman, was filed in 2011 as the Brown family challenged Utah's state laws that illegalizes polygamy.
The case won in district court but was moved up to the U.S. Court of Appeals for the Tenth Circuit and dismissed. The court ruled in 2016 that because Utah officials typically don't pursue polygamists within the state unless another crime (welfare fraud, sexual misconduct) is associated with it, the Browns lacked legal standing as they had no credible fear of persecution.
The family belongs to the Apostolic United Brethren, a Mormon fundamentalist group that supports polygamy. Brown is currently married to four women — Meri Caroline Brown, Janelle Brown, Christine Ruth Brown and Robyn Alice Brown. Together the five have 18 children.