  We exploit high quality photometry from the EVEREST pipeline to evaluate
false-positive exoplanet candidates from the K2 mission. We compare the
practical capabilities of EVEREST's pixel-level decorrelation scheme to the
data analysis pipelines widely used at the time of these planet candidates'
discovery. Removing stellar variability from the EVEREST-corrected light
curves, we search for potential secondary eclipses. For each object exhibiting
a secondary eclipse, we compare the implied brightness temperature of the
planet candidate to its calculated equilibrium temperature. We thereby identify
objects whose brightness temperature is too high to be consistent with a
planet. We identify seven systems previously flagged as planetary candidates in
preliminary vetting pipelines, and use EVEREST to instead identify six of them
as eclipsing binaries. We also project the importance of optimal photometric
vetting for TESS data. We find that the majority of blended eclipsing binaries
could be identified using TESS photometry, and a systematic study of that kind
could in principle also yield valuable information on the mass ratio
distribution in stellar eclipsing binaries.
