Yes, that is a very valid point. It really depends on what your tank chemistry is now. My outside pond has a pH of 9 and every time I have a heavy downpour, I have to rush outside and add (treated) tap water (pH 9) to the pond to undo the effect on pH by the ~neutral rain water.
I know it sounds crazy but that is the difference between a stable system vs a transient change. The outside change while coming from a harmless source might change the stable state by such a large extend that it becomes harmful to the fish. If you want to use rain water, make sure you have a good supply of it and that you make a whole hearted change and no just one week rainwater, next week tap water arrangement.

Another thing to consider is that the pure rainwater will not have much electrolytes in it so you will have to add some in as the fish needs minerals and electrolytes as well.