Because those "heightened privacy rules" would not apply or not apply in the same way to heterosexual personnel. That is discrimination.
The DADT policy since its implementation has been the transition, although not an official one.
Under DADT, especially within the last decade, only a person's CO could initiate an investigation into a person's sexuality. And unless there was some official record that actually proved a person was homosexual, a CO could choose to not investigate a person who even stated multiple times and the COC even believed was gay. Which means that every person joining the military should understand that they will be serving with homosexuals, even some who can say that they are homosexual. It would completely depend on the chain of command as to whether the person is discharged or even investigated for simple statements of homosexuality or even public displays out of uniform.
This is a transition from the old policy, which was essentially, if you were suspected of being homosexual, anyone could call you out on it. And if the CO knew about it, not only would he violate the policy of no homosexuals, but also, the person made a false official statement since they used to officially ask about a person's sexuality.