But no one pretends that courts decide in the "fact" - they just determine who is "guilty" of murder. In the US, for example, you have to be certain up to the standard of "beyond reasonable doubt", but even that standard, albeit high, means that the court don't establish facts, but only what the fact is most likely to be.

How can you be guilty of murder if you did not, in fact, kill the victim? Absolute certainty is an illusion. The word "fact" is never meant literally by people who've thought about the subject for a while.