The Duggars need to lose the obsession with being on TV and start paying attention to what's going on at home. They don't seem to understand the reality of child abuse, and their denial of the gravity of what their son did and how they handled it is just going to make life harder for their children.
By giving the interview, the Duggars have increased public scrutiny against them. They had a TV show that showed them as an "all American family" and now we find out that their son molested his two sisters among others? Their son should have been incarcerated or at least hospitalized when this happened. What other secrets are they keeping?
Lots of people don't like the Duggars for various reasons, and it seems as though they've used the criminal behaviour of one of their children as ammunition against a reality TV family whose values they don't care for. In that context, the Duggars didn't do more damage to themselves as they behaved appropriately and didn't say anything outlandish, but some people will use it as an excuse to demonise them further.
I think that while it's possible that their interview may have caused some damage for their reputation among people who watched. More importantly though they have a large base of big fans who have already decided to look past any wrong doings and continue to support and follow them. In the past negative aspects of their lives have come to the public (never in such a large way admittedly) and they have always retained their core fans. Whether or not people agree with their lifestyle and decisions they will always have some popularity if only as a spectacle.