We present the first results from a near-IR spectroscopic campaign of the Cl1604 supercluster at z~0.9 and the cluster RX J1821.6+6827 at z~0.82 to investigate the nature of [OII] 3727A emission in cluster galaxies at high redshift. Of the 401 members in the two systems, 131 galaxies have detectable [OII] emission with no other signs of current star-formation, as well as strong absorption features indicative of a well-established older stellar population. The combination of these features suggests that the primary source of [OII] emission in these galaxies is not the result of star-formation, but rather due to the presence of a LINER or Seyfert component. Using the NIRSPEC spectrograph on the Keck II 10-m telescope, 19 such galaxies were targeted, as well as six additional [OII]-emitting cluster members that exhibited other signs of ongoing star-formation. Nearly half (~47%) of the 19 [OII]-emitting, absorption-line dominated galaxies exhibit [OII] to Ha equivalent width ratios higher than unity, the typical value for star-forming galaxies. A majority (~68%) of these 19 galaxies are classified as LINER/Seyfert based on the emission-line ratio of [NII] and Ha, increasing to ~85% for red [OII]-emitting, absorption-line dominated galaxies. The LINER/Seyfert galaxies exhibit L([OII])/L(Ha) ratios significantly higher than that observed in populations of star-forming galaxies, suggesting that [OII] is a poor indicator of star-formation in a large fraction of high-redshift cluster members. We estimate that at least ~20% of galaxies in high-redshift clusters contain a LINER/Seyfert component that can be revealed with line ratios. We also investigate the effect this population has on the star formation rate of cluster galaxies and the post-starburst fraction, concluding that LINER/Seyferts must be accounted for if these quantities are to be meaningful.