Broke my water pump bolt. Now what? (Update - broken bolt is out)

Yeah I agree with your reasoning for why a bolt would break there. But since he got the rest of the bolts out and the water pump off, I still say it probably won't take much to get the stub out, since the aluminum, and the rest of the bolt is already gone... and the corrosion didn't seem to run down the bolt threads into the cast iron..... it's gonna be tough to heat the bolt without heating the cast iron around it if using a torch. If he had just a little more stick out id say to try and induction heater like a "bolt buster" (I actually have the competition model, the "mini doctor" at home) to heat the stub without heating the cast iron as much. I'm not sure there's enough sticking out for that to work though.
The bolt shank will turn red and expand in the cast iron long before any damage to cast The Idea is to then let the bolt cool, or spray your favorite oil to quench the temperature down. Bolt will shrink away from cast thread bore. As always, it helps to have a torch set with brazing tips for concentrated application of heat