Yes. Big-O is the worst case for the input, not for the algorithm. If the input is the expected average, then its Big-O is the upper-bound/worst-case for the average. But if the input is the worst case or just the algorithm itself, its Big-O will be an upper-bound/worst-case for the entire algorithm.

In other words, the original article's point should have been about vocabulary. Big-O is about worst-case, but sometimes it's implied that the Big-O analysis is about the algorithm's average case, not the algorithm's worst case.