mmmm... fun topic!
I think...
The person is also a mass thus they have their own self-generated non-uniform gravity field.
If there were a hollow little sphere at the center of the earth and a person was put into that little hollow sphere, they would slowly gravitate to the surface of the sphere but it would feel almost like zero gravity.
Nothing is perfect, thus even the slightest pico-unit of mass unbalance would eventually cause the person to drift to the surface.
This would also be the case if two planets of equal mass were held 10 feet apart and a person was placed exactly between them. The person's own gravity field would affect the outcome as to which surface they would eventually gravitate.
Even if a perfectly uniform solid sphere were placed inside that empty sphere at the earth’s center and the mass of the earth was perfectly uniform it would still gravitate to one side; that side being in the direction of the Sun and its gravitation field.
I think the "effect" of a hollow sphere at the center of the earth would be the closest thing to no effective earth gravity at all... if mass of the surrounding earth were perfectly uniform, it zeros itself out from all angles.
Fun thing to ponder!
TIGERESS
Edit: FYI, I didn't read any of the posts past the initial few when I wrote this... that would have made it not as much fun.