  Several studies have reported a correlation between the chemical abundances
of stars and condensation temperature (known as Tc trend). Very recently, a
strong Tc trend was reported for the $\zeta$ Reticuli binary system, which
consists of two solar analogs. The observed trend in $\zeta^2$ Ret relative to
its companion was explained by the presence of a debris disk around $\zeta^2$
Ret. Our goal is to re-evaluate the presence and variability of the Tc trend in
the $\zeta$ Reticuli system and to understand the impact of the presence of the
debris disk on a star. We used very high-quality spectra of the two stars
retrieved from the HARPS archive to derive very precise stellar parameters and
chemical abundances. We derived the stellar parameters with the classical
(nondifferential) method, while we applied a differential line-by-line analysis
to achieve the highest possible precision in abundances, which are fundamental
to explore for very tiny differences in the abundances between the stars. We
confirm that the abundance difference between $\zeta^2$ Ret and $\zeta^1$ Ret
shows a significant ($\sim$ 2 $\sigma$) correlation with Tc. However, we also
find that the Tc trends depend on the individual spectrum used (even if always
of very high quality). In particular, we find significant but varying
differences in the abundances of the same star from different individual
high-quality spectra. Our results for the $\zeta$ Reticuli system show, for
example, that nonphysical factors, such as the quality of spectra employed and
errors that are not accounted for, can be at the root of the Tc trends for the
case of individual spectra.
