Electrical System, Battery

My car has 48,000 miles. The battery died. The battery has a three year warranty. The dealer agreed to pay twenty five percent plus labor to replace the battery. I asked why the battery would be dead on a two year old car. He said high mileage. Seems to me, if the alternator is working correctly, the high mileage would keep the battery charged. The opposite of many discharges and charges that happen with city driving, which shorten a battery's life. They contend that there is no problem with the electrical system, the problem lies with the high mileage on the car. The electrical system has a five year/60,000 mile warranty. My concern is that they put this new battery in and the problem in the electrical system fails to charge the battery, but by the time it is evident, I will have passed by warranty mileage. Is the dealer correct in saying the high mileage would account for the drainage of the battery?