Their point is that in order to get log(n) access speed you need a sorted random access list, not that if you sort the items in a linked block list you can use

Their point is that in order to get log(n) access speed you need a sorted random access list, not that if you sort the items in a linked block list you can use binary search on it. They go on to explain how a database index constructs such a thing over the linked block list.