Large near-IR color excesses and emission-line spectra indicate the presence of optically thick circumstellar accretion disks and active boundary layers in young stars. We investigate whether this classic T Tauri (TT) behavior is found in one or both members of a binary system previously identified as a TT on the basis of the unresolved light. We consider the angularly resolved Brγ and, in one case, Na I, spectra of four close (13-26) TT systems. We also take into account the angularly resolved near-IR (K-L) colors of eight additional young binaries with separations between 03 and 25. We find that for all 12 systems, both components show, or have shown in the history of their observation, evidence for TT behavior. We demonstrate that this cannot be the result of random pairing of a population of single TT and weak-lined T Tauri (WT) stars. We speculate that the result that inner, AU-sized disks tend to survive for a similar length of time in both components of a close (03-26) binary suggests that a circumbinary envelope effectively regulates the common evolution of the inner disks.