That is exactly what it means. You cannot get a tattoo anywhere on the head, neck or face what so ever under any circumstance.
However, you may have one on the hand.
e. Tattoo policy
(5) Existing tattoos or brands on the hands that are not extremist, indecent, sexist, or racist, but are visible in the class A uniform (worn with slacks/trousers), are authorized.
Keep in mind that the regulation on this isn't exactly crystal clear. It states that "existing" tattoos on the hand are authorized, but to me, that says that you had to have the tattoo before you enlisted. Getting one after enlisting if it isn't documented in your medical folder seems to be a no-go as per part 6(f).
(6) Finality of determination.
(f) Determinations will be fully documented in writing and will include a description of existing tattoos or brands and their location on the body. A copy of the determination will be provided to the soldier. Unless otherwise directed by the Army Deputy Chief of Staff, G-1, these determinations are final. If a tattoo or brand is discovered to violate this policy after an initial determination has been documented, commanders must submit requests for an exception to policy or for discharge through the soldier’s chain of command to the MACOM for approval. Appeals to the MACOM decision will be forwarded to the Army Deputy Chief of Staff, G-1 for decision.
