Accurate broadband coverage data is essential for public policy planning and government support programs. In the United States, the Federal Communications Commission is responsible for maintaining national broadband coverage data. Observers have panned the FCC's broadband maps for overstating availability, due to coarsegrained data collection and a low coverage threshold. We demonstrate a new approach to building broadband coverage maps: automated large-scale queries to the public availability checking tools offered by major internet service providers. We reverse engineer the coverage tools for nine major ISPs in the U.S., test over 19 million residential street addresses across nine states for service, and compare the results to the FCC's maps. Our results demonstrate that the FCC's coverage data significantly overstates the availability of each ISP's service, access to any broadband, connection speeds available to consumers, and competition in broadband markets. We also find that the FCC's data disproportionately overstates coverage in rural and minority communities. Our results highlight a promising direction for developing more accurate broadband maps and validating coverage reports.