It’s not actually about being specific per se - it’s about overtly mentioning details that are already assumed from context. Grice’s maxims of quantity and relevance say that speakers only provide information when that information is important in some way and relevant to the discussion, so providing information that would otherwise be assumed means that information must be actively relevant to the conversation in some important way that warrants it being mentioned.

Yes, I didn’t found him dead. He was definitely not in the basement and he was enjoying his family

There’s a great video by Tom Scott on this exact topic.