Just because the government knows you cheated on your wife (because it came up in your background clearance check) does not mean that your wife knows. This is leverage.
I used work at such a place. If it came up during a background check that you were having an affair, they would call both you and your wife into the security office and tell the person with the clearance, "you tell them or we will". They cared less about what you did and more for if you could be blackmailed for it.