I think you’re confusing ignorance with other people’s beliefs about that agent’s ignorance. In your example of the police or the STD test, there is no benefit gained by that person being ignorant of the information. There is however a benefit of other people thinking the person was ignorant. If someone is able to find out whether they have an STD without anyone else knowing they’ve had that test, that’s only a benefit for them. (Not including the internal cognitive burden of having to explicitly lie.)
I think you’re confusing ignorance with other people’s beliefs about that agent’s ignorance. In your example of the police or the STD test, there is no benefit gained by that person being ignorant of the information. There is however a benefit of other people thinking the person was ignorant. If someone is able to find out whether they have an STD without anyone else knowing they’ve had that test, that’s only a benefit for them. (Not including the internal cognitive burden of having to explicitly lie.)