  The propagation of light beams is well described using the paraxial
approximation, where field components along the propagation direction are
usually neglected. For strongly inhomogeneous or shaped light fields, however,
this approximation may fail, leading to intriguing variations of the
light-matter interaction. This is the case of twisted light having opposite
orbital and spin angular momenta. We compare experimental data for the
excitation of a quadrupole transition in a single trapped $^{40}$Ca$^+$ ion by
Schmiegelow et al, Nat.\ Comm.\ 7, 12998 (2016), with a complete model where
longitudinal components of the electric field are taken into account. Our model
matches the experimental data and excludes by 11 standard deviations the
approximation of complete transverse field. This demonstrates the importance of
all field components in the interaction of twisted light with matter.
