Total melting of all global ice would raise sea levels by approximately 65 to 70 meters, which is far below the depth and scale required to flood the Grand Canyon (whose rim sits over 1,500 meters above sea level).
The claim compares the potential global sea-level rise from complete deglaciation (roughly 65-70 meters based on combined ice sheet volumes) against the extreme depth and elevation of the Grand Canyon. Because the physical dimensions of the Grand Canyon dwarf any possible sea level rise by more than an order of magnitude, this is a matter of straightforward geographic and mathematical comparison that requires no empirical citation of retrieved papers.