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We demonstrate the result stated in the title, thus answering an openquestion asked by Julio Becerra Guerrero, Gin\'es L\'opez-P\'erez and AbrahamRueda Zoca in J. Conv. Anal. \textbf{25}, no. 3 (2018).

The diametral strong diameter 2 property of Banach spaces is the same as the Daugavet property