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Despite advances in observational techniques, theoretical models, and computational techniques to study and simulate how galaxies form and evolve over cosmic time, underlying physical processes that determine how galaxies assemble stellar mass are not fully understood. Optical spectroscopic measurements show that gas in dusty, starbursting galaxies known as ultra-luminous infrared galaxies (ULIRGs) in the local universe have a significantly lower metal content than that of gas in star-forming galaxies with similar masses. This low metal content of gas has resulted in the claim that ULIRGs are primarily fueled by metal-poor gas falling into those galaxy merger systems from large distances. Here we report a new set of gas-phase metal abundance measurements in local ULIRGs using emission lines at far-infrared wavelengths tracing oxygen and nitrogen. Using new data from SOFIA and archival data from Herschel Space Observatory, we find that ULIRGs lie on the Fundamental Metallicity Relation (FMR) determined by stellar mass, metal abundance, and star formation rate as the key observational parameters. Instead of metal-poor gas accretion, the new data suggest that the under-abundance of metals derived from optical emission lines is likely due to heavy dust obscuration associated with the starburst. As dust-obscured, IR-bright galaxies dominate the star-formation rate density of the universe during the peak epoch of star formation, we caution the use of rest-frame optical measurements alone to study the metal abundances of galaxies at redshifts of 2-3.