Why is boiled amylase a better control than replacing he enzyme with an equal quantity of distilled water?

Answer 1

So you still have the same amount of particles with the same weight. They are just inactivated now. In your experiment, you want to make sure that it isn't the lack of particles that causes a result (as some reactions are dependent on the amount of solute (osmosis)).

Answer 2

The best control is the same composition of material, but with one inactivated through mutation or heat. That way you can be sure that other things in the reaction aren't causing the observed phenomina.