I'm pretty sure the whole point is that the planet has to be spinning fast enough that the apparent gravity on the inside equator is roughly equal to the actual gravity on the outside of the equator.
That's not correct, but it's a deceptive trick. The governing condition is that the surface is equipotential after you include both the gravitational and centripetal fields. It's tempting to then think that gravity will be constant over the surface, but that's not what equipotential means. Gravity is always normal to the surface (straight "up"), but it is allowed to vary in strength. This actually happens for Saturn, where the gravity on poles versus equator felt by someone standing there (not that you can stand there) differs by around 10%.
