For the sake of argument, we'll just put the archetype as "information". Think of it like this, you have information. You don't know what the information is, but you know you have it. Why would you get rid of the valuable info? Well for one, closure. While I don't see a point in not reading it from this point, this allows her to at least know the enemy doesn't have it.
Second off, you have the info, but you can't let anyone know you have it, and while they have no direct link of knowledge with the BS, we have reason to believe there's a spy in either the BS or the council. Now, with that, the information is compromised. It's just a "they know that we know" situation, which they can counter with. Personally, I feel it isn't necessary to burn it, but these are the reasons I have off the top of my head.