This is my understanding after digesting the explanations given by "Chambers". : )Where have you found this statement? "The next week" does not mean a period starting from the present moment.
BTW, you're absolutely right, teia_petrescu. But what you and Harry emphasise is on the "direct and indirect speech with "next week" and "the next week". However, I thought that was not what Mohaimel wanted. : (