They made the choice to put themselves on TV. No one forced them. The Duggars passed themselves off as being saved.
We have a right to question if Josh Duggar was falsely saved or if he was saved at age 7-8 but then later backslid, or if any of them are truly saved now or are falsely saved now and fooling others.
By your standard no one who commits an act of sin after they profess Christ as Savior is/remains saved.
For every little white lie you tell, or maybe you break the law and exceed the speed limit, or maybe you commit a little lust in your heart....in your opinion you are not saved.
That's the standard you're holding Duggar to. If your standards are to be used, then no one is saved or could ever be saved and remain saved. It would be a continuous cycle over and over and over again always wondering if you were or were not saved.