No, f = O(n log n) means that f doesn't grow significantly faster than n log n. That is true for f = n log n, but it's also true for f = n. The "or better" is implicit by using big-O.
Note that this wouldn't be true if the standard said that it has to be Θ(n log n).
Note that this wouldn't be true if the standard said that it has to be Θ(n log n).