I would not recommend pouring down rainwater or well/surface water down a Berkey filter and expect it to filter out everything. It is meant to filter out already disinfected water. There may be microorganisms present in water you're trying to filter. Reverse osmosis units are better at handling these types of situations, but they too carry warnings to disinfect the water before or after filtration before consuming. I would get a RO system and put a uv disinfector downstream, just to be safe.
Municipalities are required to disinfect the water by having 1 ppm of chlorine at the consumers faucet. Furthermore, EPA enforces primary standards for a variety of contaminants in city water. Rain/Surface/Well water cannot be regulated like this.