I guess your school sucked. Red-black trees ARE binary search trees. Also: the worst case behavior of a hash table is in fact worse than that of a balanced (red-black tree, b-tree, avl-tree) search tree.
Agreed. However the original poster said binary tree, a specific structure whose worse case behavior is O(n) just like a hash table.
They didn't say binary search tree (which as you observe may refer to one of several possible structures).