Yours is a hideously naive statement; your "fact" is nothing of the
kind. Light is an electromagnetic wave, period. If you change the
speed of light, you must also change the fundamental electric and
magnetic properties of the vacuum. Spacetime curvature doesn't change
those properties. Light that approaches a gravitational source gains
energy (decreases in wavelength, increases in frequency). Light that
goes away from a gravitational source loses energy (increases in
wavelength, decreases in frequency). The photons themselves are not
measured to speed up or slow down. Light is affected by gravity, but
not in the way you believe it is.