The act of taking something implies that you know it exists. It's impossible to take something you do not know it exists.The link states that plagiarism would be taking someone else's work (knowingly or unknowingly) and claiming it was your own.
Your original interpretation of plagiarism is correct. If you by chance write the exact same text as somebody else without knowing that text, it is not plagiarism. - The chances of that happening are indeed extremely slim for most texts and it would be very hard to prove.