  Oxygen is the most abundant "metal" element in stars and in the cosmos. But
determining oxygen abundances in stars has proven challenging, because of the
shortage of detectable atomic oxygen lines in their optical spectra as well as
observational and theoretical complications with these lines (e.g., blends, 3D,
non-LTE). Nonetheless, Ting et al. (2017) were recently able to demonstrate
that oxygen abundances can be determined from low-resolution (R$\simeq$2000)
optical spectra. Here we investigate the physical processes that enable such a
measurement for cool stars, such as K-giants. We show that the strongest
spectral diagnostics of oxygen come from the CNO atomic-molecular network, but
are manifested in spectral features that do not involve oxygen. In the outer
atmosphere layers most of the carbon is locked up in CO, and changes to the
oxygen abundance directly affect the abundances of all other carbon-bearing
molecules, thereby changing the strength of CH, CN, and C$_2$ features across
the optical spectrum. In deeper atmosphere layers most of the carbon is in
atomic form, and any change in the oxygen abundance has little effect on the
other carbon-bearing molecules. The key physical effect enabling such oxygen
abundance measurements is that spectral features in the optical arise from both
the CO-dominant and the atomic carbon-dominant regions, providing
non-degenerate constraints on both C and O. Beyond the case at hand, the
results show that physically sound abundances measurements need not be limited
to those elements that have observable lines themselves.
