In 2008, Granett et al. claimed a direct detection of the integrated Sachs-Wolfe (iSW) effect, through the stacking of CMB patches at the positions of identified superstructures. Additionally, the high amplitude of their measured signal was reported to be at odds with predictions from the standard model of cosmology. However, a closer inspection of these results prompts multiple questions, more specifically about the amplitude and significance of the expected signal. We propose here an original theoretical prediction of the iSW effect produced by such superstructures. We use simulations based on GR and the LTB metric to reproduce cosmic structures and predict their exact theoretical iSW effect on the CMB. The amplitudes predicted with this method are consistent with the signal measured when properly accounting the contribution of the non-negligible (and fortuitous) primordial CMB fluctuations to the total signal. It also highlights the tricky nature of stacking measurements and their interpretation.