HashSet vs LinkedHashSet

The answer lies in which constructors the LinkedHashSet uses to construct the base class:

public LinkedHashSet(int initialCapacity, float loadFactor) {
    super(initialCapacity, loadFactor, true);      // <-- boolean dummy argument
}

...

public LinkedHashSet(int initialCapacity) {
    super(initialCapacity, .75f, true);            // <-- boolean dummy argument
}

...

public LinkedHashSet() {
    super(16, .75f, true);                         // <-- boolean dummy argument
}

...

public LinkedHashSet(Collection<? extends E> c) {
    super(Math.max(2*c.size(), 11), .75f, true);   // <-- boolean dummy argument
    addAll(c);
}

And (one example of) a HashSet constructor that takes a boolean argument is described, and looks like this:

/**
 * Constructs a new, empty linked hash set.  (This package private
 * constructor is only used by LinkedHashSet.) The backing
 * HashMap instance is a LinkedHashMap with the specified initial
 * capacity and the specified load factor.
 *
 * @param      initialCapacity   the initial capacity of the hash map
 * @param      loadFactor        the load factor of the hash map
 * @param      dummy             ignored (distinguishes this
 *             constructor from other int, float constructor.)
 * @throws     IllegalArgumentException if the initial capacity is less
 *             than zero, or if the load factor is nonpositive
 */
HashSet(int initialCapacity, float loadFactor, boolean dummy) {
    map = new LinkedHashMap<E,Object>(initialCapacity, loadFactor);
}