Is Zakat sufficient if it becomes clear after its distribution that its recipient was wealthy?

Zakat is considered valid if it is given to a rich person whom the giver believes to be poor, and this is the view of the Hanbalis. Evidence for this is the hadith about the man who gave charity to a rich person, and his charity was accepted. However, if the giver pays Zakat to someone he believes is eligible (such as a Muslim), but it turns out that they are not eligible (such as a disbeliever), then the Hanbalis hold that it is not valid. Sheikh Ibn 'Uthaymeen, however, chose the view that it is valid, because the giver feared Allah as much as he was able.