At the same time with writing my answer about black holes and other mumbo jumbo, I am also intuitively feeling that something must be wrong with it. There must be a way to visualize the equivalence principle also applying for light and it should not involve us falling in a black hole...
If we assume uniform gravity and a perfectly flat surface, we can decrease the height we run our experiment from so the time it takes the stone to fall is smaller and smaller, thus also limiting how far the light can go, so obviously we do not need a surface as huge as to create a black hole or even make its curvature obvious...
Well, it seems we have to get really precise, but it is a thought experiment anyway, so why not?
A micro-meter height gives us a 135km distance, a nanometer gets it down to 4.3 km (see formula).
(You can play around with the calculation in google :p or maybe wolfram alpha if you are less lazy than me.)
Those distances may seem small enough, but a planet's curvature over them is still huge... the vertical displacement of our "ground" if it were not flat but had a radius like our earth at those 4.3km away for the nanometer height test is almost 3 meters.
In the end, if we had some super flat surface and a super-uniform gravity field so it looked like it was perpendicular to it over a sufficient length, I guess we could see a light ray falling to the surface same as a stone. But then we could also say that we have an infinitely massive gravity source an infinite distance away from us, or who knows what... is that just like if we are at a black hole event horizon again?
I never imagined a thought experiment could fail before, but here we are, folks.