HIV is NOT curable, but it can be managed.
With your semantics, yes "viral elimination" is possible. However, HIV does not live as a virus in the body until just before it breaks from the cell and is released. HIV lives as an integrated part of your DNA in infected cells.
If ozone works (not saying it does or does not), and if you can get it into the cell, it can kill the viruses that the cell is making. This does NOT mean you are killing the HIV though, because the Ozone will not destroy the cell's DNA (which is where the HIV lives). This is the problem and beauty with HIV and other RT parasites. They can integrate themselves with a host, without killing the host for long periods of time, leading to better chances of infecting another host and survival of the virus. And since they are integrated with the host DNA, the only way of killing the virus is to kill the host as well. In evolutionary terms, HIV is one of the best viruses nature can create, which is what makes it so problematic.
Now, many things can be done to keep your viral load low and your disease under control, but HIV can never be "cured". This is not to be all doom and gloom, you can live an almost normal life with HIV if you treat it correctly. However, the ONLY way to live without HIV is to never have gotten it in the first place.