We present a combined analysis of rest-frame far-UV (FUV; 1000-2000 A) and rest-frame optical (3600-7000 A) composite spectra formed from very deep Keck/LRIS and Keck/MOSFIRE observations of a sample of 30 star-forming galaxies with z= 2.40 + or - 0.11, selected to be broadly representative of the full KBSS-MOSFIRE spectroscopic survey. Since the same massive stars are responsible for the observed FUV continuum and for the excitation of the observed nebular emission, a self-consistent stellar population synthesis model should simultaneously match the details of the FUV stellar+nebular continuum and-when inserted as the excitation source in photoionization models-predict all observed nebular emission line ratios. We find that only models including massive star binaries, having low stellar metallicity ( Zlow */Z sub(middot in circle)Asymptotically = to 0.1) but relatively high nebular (ionized gas-phase) abundances ( Z sub(nch)/Zmid dot in circle sub(middot in circle)Asymptotically = to 0.5), can successfully match all of the observational constraints. We show that this apparent discrepancy is naturally explained by highly super-solar O/Fe (Asymptotically = to4-5 (O/Fe)Asymptotically = to), expected for a gas whose enrichment is dominated by the products of core-collapse supernovae. While O dominates the physics of the ionized gas (and thus the nebular emission lines), Fe dominates the extreme-UV (EUV) and FUV opacity and controls the mass-loss rate from massive stars, resulting in particularly dramatic effects for massive stars in binary systems. This high nebular excitation-caused by the hard EUV spectra of Fe-poor massive stars-is much more common at high redshift (z> ~ 2) than low redshift due to systematic differences in the star formation history of typical galaxies.