Yes, this is correct. The class that is calling the private method is the same that is declaring it. It doesn't matter that it may or may not instantiate a child class. You just can't have any code in the child class calling the private method of the parent.
In other words:
class Foo {
protected function bar() {
$this->baz();
}
private function baz() { }
}
class Bar extends Foo {
protected function bar() {
parent::bar(); // <-- works
parent::baz(); // <-- doesn't work
}
}