When someone announces an incoming "fun fact" in normal conversation, it's very annoying to the normal people who just want to follow the flow of the conversation. A fun fact is always never about the fact. It is about the presenter trying to look smart. 

If someone knows too many "fun facts", you probably know because they never seem to shut up about them. They have so many. Why? How desperate are they to look smart?

Instead of throwing out fun facts, wait until someone asks you about something you know and simply provide the answer. This is why "fun facts" are presented in guided tours; the audience is on the tour and is awaiting fun facts about whatever the tour is about. But a non sequiter fun fact about the paintings of an obscure impressionist in the middle of a zoo bus tour is not "fun". It is annoying. And even if you happen to have a fun fact related to the animals on the tour, keep it to yourself unless you are the tour guide.

The rule is simple: never show your cards.