I've heard this but I've personally been typing this way for 25+ years (wrists on the rest, including on laptops exclusively for the last 15) and my wrists are fine. Meanwhile people I know with ergonomic keyboards and everything that's supposed to save your wrists are the ones with bad wrists.
The reasonable takeaway from that correlation is that people with preexisting issues turn to ergonomic keyboards to avoid worsening those issues, not the other way round.