the zinc does not ooze over the iron to cover the scratch.
it simply provides an easier reaction alternative than the Fe
think of it like lightning ... there may be a tall concrete slab that is higher but nearby, lower down there might be a nice metal pole going deep into the ground...
the lightning will hit the pole rather than the concrete slab because it is easier to travel through the metal than the concrete.
Similarly the reaction with Zn is much easier than with Fe and as such that reaction will occur first, even if the Fe is exposed and us closer to the oxidant.
A cool application of this concept is Mg or Zn being bolted onto ships to protect the iron. A few strategicly placed big chunks of Zn or Mg bolted onto a massive hull will protect the entire hull from corrosion until of course there is no more anode material left, at which point the Fe becomes the anode again and begins oxidising...
Your water heater is another example of this - it is protected by a MG rod in the centre - when this is eaten away bye bye water heater (as the case is next on the oxidation menu)