Scaling laws of dust, HI gas and metal mass with stellar mass, specific star formation rate and metallicity are crucial to our understanding of the buildup of galaxies through their enrichment with metals and dust. In this work, we analyse how the dust and metal content varies with specific gas mass ($M_{text{HI}}$/$M_{star}$) across a diverse sample of 423 nearby galaxies. The observed trends are interpreted with a set of Dust and Element evolUtion modelS (DEUS) - incluidng stellar dust production, grain growth, and dust destruction - within a Bayesian framework to enable a rigorous search of the multi-dimensional parameter space. We find that these scaling laws for galaxies with $-1.0lesssim log M_{text{HI}}$/$M_{star}lesssim0$ can be reproduced using closed-box models with high fractions (37-89$%$) of supernova dust surviving a reverse shock, relatively low grain growth efficiencies ($epsilon$=30-40), and long dus lifetimes (1-2,Gyr). The models have present-day dust masses with similar contributions from stellar sources (50-80,$%$) and grain growth (20-50,$%$). Over the entire lifetime of these galaxies, the contribution from stardust ($>$90,$%$) outweighs the fraction of dust grown in the interstellar medium ($<$10$%$). Our results provide an alternative for the chemical evolution models that require extremely low supernova dust production efficiencies and short grain growth timescales to reproduce local scaling laws, and could help solving the conundrum on whether or not grains can grow efficiently in the interstellar medium.
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