The Fe Kalpha emission line is the most ubiquitous feature in the X-ray spectra of active galactic nuclei (AGN), but the origin of its narrow core remains uncertain. Here, we investigate the connection between the sizes of the Fe core emission regions and the measured sizes of the dusty tori in 13 local Type 1 AGN. The observed Fe K emission radii (R_fe) are determined from spectrally resolved line widths in X-ray grating spectra, and the dust sublimation radii (R_dust) are measured either from optical/near-infrared reverberation time lags or from resolved near-infrared interferometric data. This direct comparison shows, on an object-by-object basis, that the dust sublimation radius forms an outer envelope to the bulk of the Fe K emission. R_fe matches R_dust well in the AGN with the best constrained line widths currently. In a significant fraction of objects without a clear narrow line core, R_fe is similar to, or smaller than the radius of the optical broad line region. These facts place important constraints on the torus geometries for our sample. Extended tori in which the solid angle of fluorescing gas peaks at well beyond the dust sublimation radius can be ruled out. We also test for luminosity scalings of R_fe, finding that Eddington ratio is not a prime driver in determining the line location in our sample. We discuss in detail potential caveats due to data analysis and instrumental limitations, simplistic line modeling, uncertain black hole masses, as well as sample selection, showing that none of these is likely to bias our core result. The calorimeter on board Astro-H will soon vastly increase the parameter space over which line measurements can be made, overcoming many of these limitations.
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