I have asked this question on physics stackexchange and been met with a deafening silence. So I will try it here. From the modern point of view about renormalization ,super-renormalizable terms are not as innocent as they may seem. This is what I am not sure I understand and would like clarity. Is this because from the point of view of some UV theory when we let the rg flow the "relevant" operators get multiplied by positive powers of the cut off in the lower energy theory but this is bad because the cut-off can be made as high as needed and so we end up with couplings that can be made large in the lower energy theory where supposedly perturbation theory was valid? If the above is correct does this mean that there is some fine-tuning in the high and or low energy theory, or does this mean the Lagrangian in the high energy theory has a symmetry that forbids these "relevant" operators.