First, getting angry about notation or terminology is not a healthy habit. I take the approach to always try to learn when I am reading a piece of mathematics, not to get upset about how the author has expressed him(her)self.
Most authors stay away from the word 'Fact' unless assuming a mature audience. In this context, the word 'fact' is (usually) equivalent to a Theorem, i.e. by stating a fact one will be stating a theorem, but without providing a proof or an introduction to the theorem.
It is perfectly valid, once having proven a theorem, to continue and say 'now, as shown above, it is a fact that ...', as long as it is clear and the audience understands.