He's functionally right though, a remotely served interface can be implemented as a TUI behind ssh, or it could be implemented as a website. Which is the better option depends on the context, but they're both serving the same function, and the terminal emulator you're using to view the TUI is most certainly rendering it on your computer.

An X server also normally renders things locally, as does a VT-compatible terminal. If you want no local rendering at all, there's VNC.

With a web app, you can slice and dice processing between local and remote by running JS locally. Most processing usually happens remotely though, and only the display and command logic is run in the browser.