Nobody owes it to you to believe what you say either, but they offered you the chance to back up your words.

Granted they weren’t nice about it, but shit for shit leaves everyone covered in shit.

On a more serious note: If anyone can just claim anything in a conversation, that would be detrimental to any discussion. Either everybody makes up their own “facts” because no-one bothers proving everyone else’s version of a story (which is just everybody lying in everybody’s face); or everybody is constantly fact-checking everyone else, which makes the conversation take much longer than necessary.

You already have the source, or at least an idea in which context you got the information and how to find it again. It’s just common courtesy to share it the others rather than making them do the work, too.

Also: https://en.wikipedia.org/wiki/Burden_of_proof_(philosophy)