Chemical methods use toxic chemicals such as chlorine to kill pathogens in the water. They do not remove particulate matter, and some pathogens my remain protected within particles.
Radiation affects cells in 4 ways:
People walk out in the sun, get hit by radiation, and the top 3 things happen all the time. It doesn't matter because we have a lot of cells and the extras will pick up the slack. Sometimes radiation destroys DNA in such a way that the cell produces mutant cells. Most of the time these cells can't reproduce. In rare cases those cells are cancerous.
However, for single cell organisms, radiation is ends them. Most pathogens in water are single cell, so expose the water to enough radiation, and most of the pathogens won't be able to do anything harmful. Those left over will get taken care of by your digestive system. In order for a pathogen to make you sick, it must be present in significant numbers and also be able to quickly reproduce in your body. A bunch of sterile pathogens will just get digested.
Will radiation make mutant super-pathogens?
The SteriPen makes water safe to drink by exposing it to UV radiation.
The sun is a huge source of radiation in all forms. Water exposed to sunlight will be exposed to pathogen-killing radiation.