We analyse in detail the role of additional hadron-hadron interactions in elastic photon-initiated (PI) production at the LHC, both in $pp$ and heavy ion collisions. We first demonstrate that the source of difference between our predictions and other results in the literature for PI muon pair production is dominantly due to an unphysical cut that is imposed in these latter results on the dimuon-hadron impact parameter. We in addition show that this is experimentally disfavoured by the shape of the muon kinematic distributions measured by ATLAS in ultraperipheral PbPb collisions. We then consider the theoretical uncertainty due to the survival probability for no additional hadron-hadron interactions, and in particular the role this may play in the tendency for the predicted cross sections to lie somewhat above ATLAS data on PI muon pair production, in both $pp$ and PbPb collisions. This difference is relatively mild, at the $sim 10%$ level, and hence a very good control over the theory is clearly required. We show that this uncertainty is very small, and it is only by taking very extreme and rather unphysical variations in the modelling of the survival factor that this tension can be removed. This underlines the basic, rather model independent, point that a significant fraction of elastic PI scattering occurs for hadron-hadron impact parameters that are simply outside the range of QCD interactions, and hence this sets a lower bound on the survival factor in any physically reasonable approach. Finally, other possible origins for this discrepancy are discussed.
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