Levine concedes the point about black labor and blacks in auxillary services providing material support to the Confederate cause. As he says (I believe), no one contests those statements. I can't think of anyone who does.
Mythology arises when advocates of Black Confederate myth begin listing armed companies, battalions and regiments formed of slaves and FMoC in Confederate service. Some advocates of BCM will cite the Tennessee act you posted as evidence of black men were being enrolled in military service and being paid the same for service as whites. Of course both statements are false, but doesn't that version read better?
In order to stop repeating ourselves needlessly, let's agree that tens of thousands of blacks and FMoC supported the Confederate cause in a wide variety of non-combat roles.
Let's deal with the myth of the Black Confederate fighting man.
For what it's worth nearly all debates of BCM follow the same course that we are following.