what's the advantage of using factory method pattern over simple factory?

I am reading about factory method pattern and simple factory. turns out As I can understand, simple factory is enough and I don't see the use case of factory method pattern. Please read this link, https://www.binpress.com/factory-design-pattern/ , and I'll ask my questions.

1) in simple factory , it says it's bad because it violates the open/closed principle. I understand that but in factory method pattern what it did still violates the open/closed principle.

if ('car'==$toyName) {
            $toy = new NyCar();
        } else if ('helicopter'==$toyName) {
            $toy = new NyHelicopter();
        }

If there'll be a new tory for New York, we need to add it here.

2) after reading the link, before it actually reached the better solution, it used this following code. :

class NySimpleFactory {
    public function createToy($toyName) {
        $toy = null;

        if ('car'==$toyName) {
            $toy = new NyCar();
        } else if ('helicopter'==$toyName) {
            $toy = new NyHelicopter();
        }

        return $toy;
    }
}

class NyToysFactory {

    public $simpleFactory;

    public function __construct(SimpleFactory $simpleFactory) {
        $this->simpleFactory = $simpleFactory;
    }

    public function produceToy($toyName) {
        $toy = null;
        $toy = $this->simpleFactory->createToy($toyName);
        $toy->prepare();
        $toy->package();
        $toy->label();
        return $toy;
    }
}

Then it says, The developers finish the new code quickly and hand it over to the US factories. After two weeks, the phone starts ringing in the developers’ office because the New York factory was having production issues. It turns out that the NyToysFactory class has been modified by developers at the remote branch because the staff doesn’t want to do packaging and labeling work. They’ve modified produceToy() by removing its label() and package() functions.

It seems like Simple Factory won’t work in this scenario. We don’t want branches in US to be able to modify produceToy() functions. ProduceToy() should consist of a set of standard procedures and the branches should only be responsible for creating location specific toys. What if they can create an abstract class? And the abstract class they create will have a concrete produceToy()method which will implement a set of standard operating procedurea that all branches have to follow. Inside produceToy(), it calls its own abstract method createToy() to obtain a toy class. This way createToy() is able to encapsulate object creation and, since it’s abstract, it delegates the creation to its subclasses.

Question is: a)What does it mean by saying handing over it to US factories? b) or We don’t want branches in US to be able to modify produceToy() functions. they can still modify produceToy function, what difference does it make at all if they can't or can change it? I just don't understand why simple factory was bad for the following example at all.

No need to read about abstract factory at that link