  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.
