If two people with identical flashlights are stationary at the top and bottom of a mountain, shining the flashlights at each other,
the top person will see the light redshifted, and the bottom person will see the light blueshifted.
It's the same for stationary observers near a black hole …
the gravitational effect of a black hole is (outside the event horizon and outside the surface of the star) exactly the same as that of a star of the same mass.