The Birthday Paradox is about a group of people sharing at least one birthday between them. If it was at least 1 person out of 23 people sharing YOUR birthday then the odds would be 1 - (364/365)^23 which is around 0.06 (or 6% chance). So, yes, this scenario is a lot less likely.
"We believe developers and users should have the flexibility to use our services as they see fit, so long as they comply with our usage policies. We're exploring whether we can responsibly provide the ability to generate NSFW content in age-appropriate contexts through the API and ChatGPT. We look forward to better understanding user and societal expectations of model behavior in this area."
When educating the general public about the risks and limitation of LLMs, I think "hallucinating" is a useful term - it is something people can understand and it conveys the idea of LLMs being somewhat random and unreliable in their responses. I'm not sure "confabulating" is so easily understood or accessible.