The pattern: subscriber SIP endpoint -> your PBX -> wholesale SIP trunk -> PSTN. The PBX terminates SIP signalling from the subscriber, re-originates SIP to the wholesale carrier, and bridges RTP between the two sides. From the carrier's perspective, every call comes from your PBX's IP. From the subscriber's perspective, the wholesaler is opaque.
This is not new technology. It is standard PBX architecture. The privacy framing matters when subscribers care about their carrier-side metadata exposure - lawyers, journalists, activists.