We assess the photometric variability of nine stars with spectroscopic Teff and log(g) values from the ELM Survey that locate them near the empirical extremely low-mass (ELM) white dwarf instability strip. We discover three new pulsating stars: SDSS J135512.34+195645.4, SDSS J173521.69+213440.6 and SDSS J213907.42+222708.9. However, these are among the few ELM Survey objects that do not show radial velocity variations to confirm the binary nature expected of helium-core white dwarfs. The dominant 4.31-hr pulsation in SDSS J135512.34+195645.4 far exceeds the theoretical cutoff for surface reflection in a white dwarf, and this target is likely a high-amplitude delta Scuti pulsator with an overestimated surface gravity. We estimate the probability to be less than 0.0008 that the lack of measured radial velocity variations in four of eight other pulsating candidate ELM white dwarfs could be due to low orbital inclination. Two other targets exhibit variability as photometric binaries. Partial coverage of the 19.342-hr orbit of WD J030818.19+514011.5 reveals deep eclipses that imply a primary radius > 0.4 solar radii--too large to be consistent with an ELM white dwarf. The only object for which our time series photometry adds support to the ELM white dwarf classification is SDSS J105435.78-212155.9, with consistent signatures of Doppler beaming and ellipsoidal variations. We interpret that the ELM Survey contains multiple false positives from another stellar population at Teff < 9000 K, possibly related to the sdA stars recently reported from SDSS spectra.
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