I think JoyfulNoise has summed this up nicely. We are not against the use of UV or Ozone systems, we just feel that they are of little or no benefit in the typical residential pool, as to the issue of reducing Chlorine use, the simple truth is it depends, with high bather loads, yes it can, but with typical residential bather loads in a well balanced pool it often increases Chlorine use.
Think about it this way, Chlorine sanitizes and oxidizes bather waste, then UV light from the sun breaks down the Chlorine. This UV from sunlight breakdown of Chlorine is what eliminates the combined Chlorine compounds from your pool (the bad stuff), it also breaks down the Free Chlorine ( the good stuff). A UV systems kills pathogens by exposing them to a wide spectrum of UV including UV-C which in nature is almost entirely blocked by our atmosphere (That Ozone layer thing), so while these UV systems do kill pathogens taking some of the work load off your Chlorine as the water passes through UV cell, it also breaks down your Chlorine. The question then becomes does it break down more or less Chlorine than would be consumed breaking down the organic compounds in your pool. In the studies from the UV sales brochure they try to convince you that it does more help than harm, however they are often starting from a pool that may have algae issues and is not properly Chlorinated, in the real world dealing with a well balanced pool the benefits become a lot more questionable.
Also while there are some pathogens that UV can eliminate nearly instantly which may take Chlorine many hours to break down, these UV systems can only kill the pathogens that passes through the UV cell, so only applies to pathogens that are free floating in the water, not clinging to some pool surface, and it takes many days for the typical pool pass nearly 100% of its water through the filtration and UV system. Even if we take the common industry standard practice of sizing pumps to filter 100% of the water every 8-12 hours, it is not like we have a full pool and an empty pool to move water between, so in that pretend 12 hour water turn over time only a fraction of the water will pass through the UV cell, another smaller fraction will pass through twice, and other smaller amount 3 times, and so forth. There is math to back this up, but lets leave it at it takes a couple of days or more for 99% of your water to pass through the UV cell, and much longer for 99.9 % or 99.99%.... by that time the Chlorine would likely have had its many hours needed to kill the pathogen.