This statement is true for higher bather-load pools such as commercial/public pools, but most residential pools are such low bather load that the ozone isn't needed. Most chlorine loss is from sunlight and the amount from bather load is negligible. Even in a smaller 7500 gallon pool, every person-hour is just 0.14 ppm FC of chlorine demand. A lot more than that is lost during the day from sunlight. Also, for outdoor pools, the UV in sunlight that breaks down chlorine produces hydroxyl radicals that are powerful oxidizers -- the same ones that ozone produces when it breaks down. They aren't enough for higher bather-load pools, but for residential pools they do fine.
You might take a look at Chemistries of Ozone for Municipal Pool and Spa Water Treatment for more info on ozone, including how it reacts with chlorine though that's normally seen more in residential spas (i.e. increased chlorine demand in between soaks in infrequently used spas).
