Guess I have but I am sure there is a word - what I am thinking of is more like the boy who cried wolf, told so many things that you become impervious to the news.
Well, there's 'infobesity', which is overload of info. and a word I rather like, but that's not quite what you mean. I'll keep thinking.
It's sort of like 'scaremongering'; isn't it?