What she wants is to have committed adultery for 8+ years (and more likely 16 years) and have no consequences. She wants to be able to "get away with it" and not have to take personal responsibility for the choices she's made.
I wholeheartedly agree that if the counselor says "Don't divulge more if you don't want to" ...
go to a different counselor! In a marriage, the whole POINT is intimacy with another person, and to be truly intimate there has to be transparency. That means I am "see through" enough to let you see the real me, warts and all. And don't fall for the claim that she needs some degree of "privacy" I throw the

flag!
Privacy=closing the bathroom door when you dress or go to the bathroom; aka modesty.
Secrecy=not revealing the True Me and purposely hiding from my spouse. There is no room for secrecy in a marriage!
I generally explain to Disloyal Spouses like this:
"You have all the pieces of the puzzle and you know what the picture is when you put all the pieces together..and the picture makes you sick because either you miss the OP and you're trying to put them out of your mind, or you are ashamed that you did that! Meanwhile though, your spouse does not have all the pieces of the puzzle and they are scrambling to try to make heads or tails of the picture. Right now, without all the pieces, all they see is the worst parts and they fill it in with EVER WORSE!" And to the Loyal Spouses I explain like this:
"Put yourself in your spouse's shoes. You did something REALLY, really stupid like embezzling...and you were caught. Now you feel like such an idiot for doing it and want nothing more than to sort of get past it and prove you can be honest again. But it's in the newspaper, all your friends talk about it behind your back, and your spouse constantly asks questions about it! 'When did you steal the first $100? What were you thinking? How long did you steal?' and all the while you know in your heart that you've see the mistake you've made and you've changed for real! But no one will let it go..." I think using those analogies, each spouse can see the position in which they are putting their own spouse.
Then I recommend for couples who are working on rebuilding that they make an agreement that will work for both of them. Reach the Mutual Understanding that the Loyal Spouse will ask only one or two questions each day and agree that the LS will discipline themselves to ONLY those 1-2 questions. Simultaneously, the Disloyal Spouse agrees to answer those one or two questions fully and honestly. After they answer, no matter what it is, agree to hug each other and say, "Thank you for being honest" so that honesty is safe. Then if you have to...go apart so you can digest what was said. Finally, reach a Mutual Understanding about how long you'll ask questions--like 30 days or 60 days. This let's the Loyal gradually get some of the puzzle pieces they need (and they're free to stop before 30 days if they're ready), and it let's the Disloyal know that it won't become the Spanish Inquisition and it won't be held over their head for forever. There WILL be an end in sight!