Don't think it works here though - if the pressure of reflected sunlight is counteracting gravity, then I don't see how the statite can be acting as a sunshade. If it were in position for that, the sunlight would be pushing it toward the Earth, no?
If anything this sounds more like the reflectors often proposed for Martian terraforming, which are designed to heat the planet rather than cool it.
But in practice, I think you're right. Forward wrote a short story about such a "pole sitter" ("Race to the Pole"), and had one of the characters say this:
The control problem of keeping the [statite] balanced over the pole is very tricky, especially during the summer season of that hemisphere when the polar axis is over on the sunlit side of the Earth. That’s why ‘pole-sitters’ have to be placed so far away from the Earth. If they get any closer than 250 Earth radii, they become unstable during the summer. [2]
[1] https://patents.google.com/patent/US5183225A/en
[2] https://www.centauri-dreams.org/2010/07/29/statites-hovering...
