On a more fundamental level, why would anyone assume that a coroutine is guaranteed to complete if it is never awaited? There is no reason a scheduler could not be totally lazy and only execute the coroutine once awaited.
At least he bothered to make note of TaskGroups, also clearly shown in his documentation screenshot, immediately above the section marked Important that went ignored, and finishes with "As long as all the tasks you spin up are in TaskGroups, you should be fine." Yep, that's all there was to it.