Yes indeed, the black hole is a dramatic exaggeration where it would be obvious to a human, but it'd be true above the Earth.
For spherical gravitational fields the speed would be:
where c is the usual speed with no gravity around and
the speed in the presence of gravity. M the Mass of the body, G is Newton's Constant and r is the radius of the observer.
For the case you mentioned that results in light being less than a m/s slower.
Edited by Son Goku, : No reason given.