  Lattice contribution to the electronic self-energy in complex correlated
oxides is a fascinating subject that has lately stimulated lively discussions.
Expectations of electron-phonon self-energy effects for simpler materials, such
as Pd and Al, have resulted in several misconceptions in strongly correlated
oxides. Here we analyze a number of arguments claiming that phonons cannot be
the origin of certain self-energy effects seen in high-$T_c$ cuprate
superconductors via angle resolved photoemission experiments (ARPES), including
the temperature dependence, doping dependence of the renormalization effects,
the inter-band scattering in the bilayer systems, and impurity substitution. We
show that in light of experimental evidences and detailed simulations, these
arguments are not well founded.
