All you'd have to do is know someone in (for example the UK ) the Home Office who can get hold of headed notepaper ( and envelopes) and simply get a draft up on Word, make it full of big words, print it out and like you say send it to all the papers/news outlets.
Trouble is though it would have to be official paper as most government offices ( that I know of) have watermarked paper.
But I agree with you sometimes people can panic over something they have no control over, like right this moment its snowing and people are panic
buying at the petrol station across the road from me.
With something like Aliens you'd have to have a good long hard think of what would work, what would look fake and what you may need to envisige as to