In the words of Brandt, "well, Dude, we just don't know."
If you need evidence that this is sufficient for dismissal, merely stating that impropriety exists is apparently enough to get my first flag on hn after 12 years.
All kinds of reasons.
The biggest risk for OpenAI is the public perception that the discretion of ChatGPT can not be trusted. If the CEO is caught using poor discretion, the public will transfer that property to the company's products.
For instance, if Tesla could fire Elon Musk, I'm sure they would have by now.