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]

4 Pages, 6 Figures. Accepted for publication in A&A