Perhaps the first safety standard OpenAI can implement itself is a warning or blog post or something about how ChatGPT is completely incapable of detecting ChatGPT-written text (there is no reliable method currently; GPTZero is borderline fraud) and often infers that what the user wants to hear is a "Yes, I wrote this", and so it doles out false positives in such situations with alarming frequency.
See: The link titled 'Texas professor fails entire class from graduating- claiming they used ChatGTP (reddit.com)', currently one position above this one on the homepage.