Controllers actually have only one responsibility: altering the applications state based on user's input.
A controller can send commands to the model to update the model's state (e.g., editing a document). It can also send commands to its associated view to change the view's presentation of the model (e.g., by scrolling through a document). source: wikipedia
source: wikipedia
If instead you are having Rails-style "controllers" (which juggle active record instances and dumb templates), then of course out are breaking SRP.
Then again, Rails-style applications are not really MVC to begin with.