The ocean is not borrowing its color from the sky; it is advertising its own. That bold claim rests on quantum interactions between light and water molecules, not on some giant mirror effect at the surface. When sunlight hits the sea, its full spectrum enters the water column, and longer red and orange wavelengths are selectively absorbed through molecular vibrational modes, leaving shorter blue wavelengths to survive the journey.
More stubborn than myth is the idea that this is just reflection. It is not. Surface reflection, or Fresnel reflection, accounts for only a small fraction of what you see when you look out from a ship or a shore; the dominant signal comes from light that has penetrated, been filtered by absorption, and then redirected by Rayleigh and Mie scattering from water molecules and suspended particles. Red light is swallowed within a few meters, while blue and green penetrate tens of meters, so the integrated return to your eye is weighted heavily toward the shorter end of the visible spectrum.
Stripped of romance, the blue ocean is a laboratory display. Each photon is sorted by wavelength through the absorption coefficient of water and the scattering phase function of the medium, turning the sea into a massive, passive spectrometer. Under thick cloud, under polar skies, even under artificial illumination, this intrinsic filtering still operates, quietly proving that the color you see belongs to the water itself.