I think this is false, screenshots and screen recording are both possible with sway for example afaik
Sway's compositor implements a way to do this as only it has access to all of the display data, but there is no standard way outside of the compositor to do this under Wayland.
The consequence of this is that every program that wants to do a screencast (Skype, Discord, etc) will have to integrate with specific compositors to do this - there is no standard way to do this across all compositors like under X.