Design Pattern semantics: Can the operation, given in example, be classifiable as a Factory Method?

Question

Describing the question without code:

If a Class' operation (that otherwise fulfills structure of Factory Method -pattern,) returns a copy of an existing object's reference, which is fetched by another object's operation, and used by it's known type, instead of instantiating a new object - can it be classified as a Factory Method?

In addition, if it is deemed as not-a-factory-method; Does it matter whether the process of creating a new instance of a ConcreteProduct happens within the ConcreteCreator, or not? (Taking account that in JAVA you always end up returning a reference, so only pragmatic difference would be that we're creating a new instance instead of using an existing one - but does this make the whole difference whether we have a "Factory Method" or not?)

A minimal example in JAVA:

interface Product { ... }
class ConcreteProductA { ... }
class ConcreteProductB { ... }

class ProductHolder
{
    private Product foo;

    /*
    * May return an instance of either ConcreteProductA or ConcreteProductB
    * Sets foo null, for attempting to mimic a composition relationship to holder, foo being moved into another composition relationship
    */
    public Product getProduct() {
        Product reference = foo;
        foo = null;
        return reference;
    }

    public void setProduct(Product foo) {
        this.foo = foo;
    }
}

interface Creator { public Product createProduct(); }

class ConcreteCreatorA implements Creator
{
    @Override
    public Product createProduct(ProductHolder holder) {
        return holder.getProduct();
    }
}

Edit: Noting that I intentionally left unchecked whether method returns null or not, does this have any relevance to the question?

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(my) Arguments for:

• (Most of all) It fulfills the GoF: Design Patterns -book's Factory Method -part's "Applicability" -section's paragraph #1:

"(Use Factory Method -pattern, when) ..CreatorClass does not know in advance, from which ProductClass the instantiated objects must be."

[Possibly an incorrect set of words; I use a translated version.]

• It does allocate memory, for holding the reference to the chosen object.
• It is typecasted to it's type, known by Creator -class.
• It is defined within ConcreteCreator -class (referencing GoF: Design Patterns -book's UML diagram).

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(my) Arguments against:

• It uses an existing object, therefore it doesn't create a new instance. (Is this necessary, semantics-wise?)
• It copies a specific object, not a specific class. (Given instance may have existing altered states, as opposed to a newly constructed instance)

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Related yet separate questions' posts:

• Is it still a factory if it shares instances across requests?

General answer to his/her question: Singleton Factory

Answer 1

Reading the code I assume there's going to be a ConcreteCreatorB, C, etc. at least some of which will really new up objects rather than reusing existing ones.

So, I guess it remains a Factory method as long as this is true. Otherwise, it's probably not one - and I can't see the point of making it look like one, giving names such as createProduct() and Creator.