The 1570 movement is for the 4-digit references like Datejust 1600, 1601, 1603, late Sub 5513, etc etc.
Is the case stamped 16013 between the lugs at 6 o'clock ? The dial looks correct (1600 series would look more like a "pie-pan") but the date font looks like it's for 1600 series (bolder).
Also the 16013 dial might be modified to sit on the 1570 movement coz the legs would not normally fit.
Frankenwatch ... maybe ?