First, some comments here are not right.
Acoustic treatment and soundproofing are completely 2 separate matters.

Acoustic treatment - makes the room sound better. In general, treatments such as wall panels, soft surfaces and bass traps.

Sound Proofing - isolating the sound source and avoid it leaking out of the enclosed area. In general, isolation to avoid vibrations travelling out of the room, such as building a suspended room inside a room.

Not gonna argue with you but I would stick to my statement. Engineering approach when you identify these 2 issues are different.
Sound proofing is not a subset of acoustic treatment as sound proofing has got to do with vibration isolation whereas acoustic treatment deals with the vibrations response within the room. In your argument I believe you meant by having particular frequencies absorbed, it reduces the energy leakage outside, which is partly true but does not mean sound proofing is a subset of acoustic treatment.

By saying soundproofing is a subset of acoustic treatment, it means you can draw a Venn diagram with Acoustic Treatment and its subset is soundproofing (which in fact you cant).