The current anti-HIV drugs are said to act by preventing fresh cycles of infection, that is by preventing the formation of new proviral DNA in previously uninfected cells, which in turn prevents the formation of new RNA within these cells and the production of new viral particles.
Thus drugs that decrease the viral load, that is, RNA, should first decrease the proviral DNA, that is, the "viral burden".
But what is found is that the viral load decreases to undetectable levels while there is no significant decrease in DNA.