Previous analyses of mid-infrared water spectra from young protoplanetary disks observed with the Spitzer-IRS found an anticorrelation between water luminosity and the millimeter dust disk radius observed with ALMA. This trend was suggested to be evidence for a fundamental process of inner disk water enrichment proposed decades ago to explain some properties of the solar system, in which icy pebbles drift inward from the outer disk and sublimate after crossing the snow line. Previous analyses of IRS water spectra, however, were uncertain due to the low spectral resolution that blended lines together. We present new JWST-MIRI spectra of four disks, two compact and two large with multiple radial gaps, selected to test the scenario that water vapor inside the snow line is regulated by pebble drift. The higher spectral resolving power of MIRI-MRS now yields water spectra that separate individual lines, tracing upper level energies from 900 to 10,000 K. These spectra clearly reveal excess emission in the low-energy lines in compact disks compared to large disks, demonstrating an enhanced cool component with T ≈ 170-400 K and equivalent emitting radius R _eq ≈ 1-10 au. We interpret the cool water emission as ice sublimation and vapor diffusion near the snow line, suggesting that there is indeed a higher inward mass flux of icy pebbles in compact disks. Observation of this process opens up multiple exciting prospects to study planet formation chemistry in inner disks with JWST.