Well the website said that as early as Nov 2022
https://web.archive.org/web/20221108...your-seat.html
All I can say is it's not true for tickets issued with Avios as late as Oct 2023 (when I redeemed my last non-160 CX ticket for May 2024 travel)
I think the difference is - Avios tickets are Amadeus and can go directly into the MMB, but Sabre cannot. Once manual, the agents get nasty.