The Short Version
This claim is true. Multiple authoritative sources — including the U.S. Geological Survey and peer-reviewed research in Nature Geoscience — confirm that fresh groundwater vastly exceeds the volume of water in all rivers and lakes combined, by roughly 100:1 or more. Even conservative estimates of fresh groundwater alone (~10.6 million km³) dwarf the ~105,000 km³ in rivers, lakes, and streams. Note that ice and glaciers still hold more freshwater than groundwater overall, but the claim's specific comparison is well-supported.