No, you are not misinformed. Both RDP and X11 can send both drawing commands and bitmaps. However, as /u/moonchild says, only older programs seems to be sending drawing commands directly. Newer programs want to be fancy and uses toolkits that do their own drawing to have visual effects. (Witness the speed of Emacs vs. editor-du-jour)
> Newer programs want to be fancy and uses toolkits that do their own drawing to have visual effects
Good toolkits like WPF and UWP implement their own drawing by utilizing Direct3D. These two are using DX 9.0c and D3D 11.0 respectively, and both are supported in RDP protocol.
If you connect to a remote PC and run dxdiag.exe there, you’ll see 3D acceleration is supported, you’ll also see the GPU driver got replaced with completely different one, it’s no longer Intel, Nvidia or AMD, but the one from MS.
This has interesting consequences, e.g. all D3D APIs which move data from system RAM or VRAM or back now become network calls, the system RAM is on the server, VRAM is on the client.
P.S. Modern web browsers use Direct2D and DirectWrite to render stuff on Windows, there’s D3D 11 underneath, i.e. RDP remote rendering is fully supported for browsers and Electron apps.