Due to their high intensity of emission in the O VI 1031.9 and 1037.6A lines, even small sunspots on the solar disk can strongly influence the intensity of the radiative scattering component of O VI lines in the corona. Observations of O VI disk spectra show a 1032/1038 line intensity ratio of >2.6 in a sunspot compared to quiet disk values of 2. The enhancement of the 1032 line in comparison to the 1038 is likely due to interaction between molecular hydrogen emission from the sunspot and the chromospheric O5+. Modeling shows that a contribution from sunspots increases the coronal O VI 1032/1038 intensity ratio to values considerably higher than those achieved with a quiet disk or coronal hole spectrum. Therefore a re-examination of flow velocities derived from UVCS/SOHO streamer observations must be made. This modeling demonstrates that the inclusion of sunspots, when present, may lead to non-zero outflow velocities at lower heights in streamer cores in contrast to some existing model results. ; Comment: 4 pages, 3 figures