That is not true, it is hard to make technical claims without corresponding knowledge.
After downloading once into the browser’s local storage, SketchUp Free is completely executed locally by your processor like the desktop version (it is not comparable to a video stream). There is the same SketchUp core inside both. In contrast to the desktop version, Free requires a browser that supports WebGL equally good as OpenGL and runs Javascript very fast (and is optimized for machine code transcompiled to JS). That is not always the case with all hardware/browser combinations.
You are right that in case of problems, SketchUp Make is a pretty good alternative, albeit that it supports less platforms.