The simple answer to the question, you boil the water to kill off any bugs in it which might turn your gallon or more of wine to which you have devoted many hours into vinegar.
Filters are good at removing dissolved chemicals and solids but bacteria can live on the filters (if we're talking of the brita kind and not 10M Ohm sterile filters for labs or even the strerile filters many breweries use). Bottled water should be ok, but it can never be guarnteed that the bottling plant didn't have some bacteria floating around on it, hence the slightly odd idea of best befores on bottles, though if the plant uses a sterile filtering process you shouldn't have any problems.