  Stellar spectroscopy provides useful information on the physical properties
of stars such as effective temperature, metallicity and surface gravity (log
g). However, those photospheric characteristics are often hampered by
systematic uncertainties. The joint spectro-seismo project (APOKASC) of field
red giants has revealed a puzzling offset between the log g determined
spectroscopically and those determined using asteroseismology, which is largely
dependent on the stellar evolutionary status. Therefore, in this letter, we aim
to shed light on the spectroscopic source of the offset using the APOKASC
sample. We analyse the log g discrepancy as a function of stellar mass and
evolutionary status and discuss the impact of He and carbon isotopic ratio.
  We first show that for stars at the bottom of the red giant branch, the
discrepancy between spectroscopic and asteroseismic log g depends on stellar
mass. This indicates that the discrepancy is related to CN cycling. We
demonstrate that the C isotopic ratio ($\rm ^{12}C/^{13}C$) has the largest
impact on the stellar spectrum. We find that this log g discrepancy shows a
similar trend in mass as the $\rm ^{12}C/^{13}C$ ratios expected by stellar
evolution theory. Although we do not detect a direct signature of $\rm ^{13}C$,
the data suggests that the discrepancy is tightly correlated to the production
of $\rm ^{13}C$. Moreover, by running a data-driven algorithm (the Cannon) on a
synthetic grid trained on the APOGEE data, we quantitatively evaluate the
impact of various $\rm ^{12}C/^{13}C$ ratios. While we have demonstrated that
$\rm ^{13}C$ impacts all parameters, the size of the impact is smaller than the
observed offset in log g. If further tests confirm that $\rm ^{13}C$ is not the
main element responsible of the log g problem, the number of spectroscopic
effects remaining to be investigated is now relatively limited. [Abridged]
