CI Tau is a young (~2 Myr) T Tauri system with a substantial near-infrared excess in its SED, indicating that the protoplanetary disk extends very close to its star. This is seemingly at odds with the radial-velocity discovery of CI Tau b, a ~12 MJ planet at ~0.1 au, which would be expected to carve a wide, deep cavity in the innermost disk. To investigate this apparent contradiction, we run 2D hydrodynamics simulations to study the effect of the planet on the disk, then post-process the results with radiative transfer to obtain an SED. We find that at ~0.1 au, even such a massive companion has little impact on the near-infrared excess, a result that holds regardless of planetary eccentricity and dust size distribution. Conversely, the observed full-disk signature in CI Tau's SED is consistent with the existence of the hot super-Jupiter CI Tau b. As our simulations uncover, clear transition-disk signatures in SEDs are more likely to be signposts of nascent "warm" Jupiters, located at around 1 AU in the future habitable zones of their host stars.