Hmmm ... I am not a fan of how that was put ... when it comes to proving things, it is not so much that from a false statement you can infer anything. Logic itself does not care whether things are true or false, and so starting with $P$ does not mean that I can infer anything, even if $P$ turns out to be false.
What is true, however, is that you can infer anything you want from a contradiction.
For example, suppose we have your standard contradiction: we have both $P$ and $\neg P$
Now, from $P$ we can infer $P \lor Q$
But if we have $P \lor Q$, and we also have $\neg P$, then we can infer $Q$
And so yes, since $Q$ can be anything at all, we can infer anything from a contradiction.
To go back to the 'false' though: If you know that $P$ is true, then if you assume that $P$ is false (i.e. you have $\neg P$), then indeed you can infer anything you want. But you can't infer anything you want from a false statement alone.