No, it is not true.
Chlorine reacts with ammonia that is present, the end product is chloramines. If you add more chlorine, you will oxidize the chloramines (and ammonia) and you will end up with free chlorine. Free chlorine does not sting and burn the eyes like chloramines do.
If you keep your pool water clean, the generation of chlorine disinfectant byproducts will be reduced.
Chlorine dioxide is considerably more difficult to use in swimming pools. Ozone has no residual disinfecting power, so it has limited use in a swimming pool.
"Can chlorine dioxide be used to disinfect swimming pools?
For swimming pool disinfection the combination of chlorine (Cl2) and chlorine dioxide (ClO2) can be applied. Chlorine dioxide is added to the water. Chlorine is already present in the water as hypochlorous acid (HOCl) and hypochlorite ions (OCl-). Chlorine dioxide breaks down substances, such as phenols. The advantages of chlorine dioxide are that it can be used at low concentrations to disinfect water, that it hardly reacts with organic matter, and that little disinfection byproducts are formed."
"What are the costs of chlorine dioxide use?
Chlorine dioxide is about 5 to 10 times more expensive than chlorine. Chlorine dioxide is usually made on site. The costs of chlorine dioxide depend upon the price of the chemicals that are used to produce chlorine dioxide. Chlorine dioxide is less expensive than other disinfection methods, such as ozone."
Unless you are talking about a large commercial pool application with staff available to do the disinfection, you are probably wasting your time considering other alternatives to chlorine.