It is true. My message you quoted was from March 20, 2023 so it doesn't address anything past that date, obviously. Prior to 2018 the basic hesalite Speedmaster was US$5,250. On Jan 1, 2018 it was increased a token $100 to US$5,350 where it remained until the new 3861 replaced it. If you look on the US website it still shows the old 1861 Speedmaster at $5,350 and even though it is no longer available the price has not increased. (Omega usually increases prices on older models even though they are no longer available. The Apollo 11 50th is no longer available but it was given a price increase last year.)
Omega's prices for the basic Speedmaster were rock steady from Jan 2018 until now for the 1861. I don't know what the prices were for the rest of the Omega line but my impression is they were steady until last year's increase which was pretty benign in the scheme of things.