Don’t blame or give Satan any undue credit here. The Duggars sinned and it’s their own fault. Had they dealt with this years ago by proper channels this would have not come back to bite them in the a$$. The tried to hide it as Numbers 32:23 says “ and you may be sure that your sin will find you out.”
You're 100% correct, and the only winner in it is Satan himself. The rest of us lose. It's a very heartbreaking situation, to be sure. I don't condone it or feel bad for him. He is getting his due here on earth, and he'll hafta deal with God later.