Can a positively charged conductor have negative surface charge density somewhere?

Our body is positively charged, so it's potential is positive.

Suppose there is a place on it's surface with a negative charge density. Electric field direction is towards the surface near the spot.

Consider some electric field line that ends on our spot. Where could it originate?

There are only two options: it originated either from some other point of the conductor or from the infinity. (*)

The first option would mean that two points of the conductor have different potentials, so it's impossible.

Second option would mean that the potential of ending point of the electric line field is negative. But it must be positive.

So there are no negatively charged regions on the surface of our body.

(*) I understand that the proof is not rigorous here, but I am quite sure I can improve it.