It's important to realize that while there are two classes, there is only one object.
So, yes, of course it inherited the private fields. They are, presumably, essential for proper object functionality, and while an object of the parent class is not an object of the derived class, an instance of the derived class is mostly definitely an instance of the parent class. It could't very well be that without all of the fields.
No, you can't directly access them. Yes, they are inherited. They have to be.
It's a good question!
Update:
Well, I guess we all learned something. Since the JLS originated the exact "not inherited" wording, it is correct to answer "no". Since the subclass can't access or modify the private fields, then, in other words, they are not inherited. But there really is just one object, it really does contain the private fields, and so if someone takes the JLS and tutorial wording the wrong way, it will be quite difficult to understand OOP, Java objects, and what is really happening.
Update to update:
The controversy here involves a fundamental ambiguity: what exactly is being discussed? The object? Or are we talking in some sense about the class itself? A lot of latitude is allowed when describing the class as opposed to the object. So the subclass does not inherit private fields, but an object that is an instance of the subclass certainly does contain the private fields.