We present moderate resolution (R = 2000), high signal-to-noise (S/N > 80) near-infared spectra of five galactic center He I emission-line stars. The nature of these stars has been difficult to ascertain in previous studies because they relied on emission features arising in the stellar wind, predominately in the 2 micron range, to determine the effective photospheric temperature. Three of the five He I emission-line stars we observed showed the 1.700 micron He I line in absorption. We argue that these three stars have less developed winds and are less evolved than the remaining broad-lined, He I emission-line stars studied previously. Instead, our three stars are better compared to normal, albeit highly luminous, B supergiant stars. We explore a possible explanation for the extremely high luminosity of the galactic center stars by applying recently developed evolutionary tracks for massive stars with high rotation.