Yea, I am normally extremely pro science, but this just seems like a REALLY bad idea. Setting aside the idea that it would become more deadly, IMO the odds of destroying enough HIV DNA to make a difference without altering human cells seems unlikely.
PS: There are 10's of million's of people with HIV, so randomly mutating trillions strands of viral HIV inside people as they are reproducing and not creating a worse strain seems unlikely.
In genetics, introducing random changes is one of the worst ways to find useful results. Admittedly, across such a large population, the virus might get worse, but if by worse you mean more deadly, then like ebola, it will restrict its growth by not transferring to as many people. If by worse you mean find another receptor that is hard to attack, then I'm not really sure what to do...
In scientific circles the idea is called "crash error". RNA viruses, like HIV and influeza (the flu), mutate very fast, because they use polimerases for their replication that lack sequence proofreading and error correction. Theoreticians have estimated that was the virus to mutate a bit faster, its complement of encoded proteins would stop being able to interact with each other, and the virus would lose the ability to recompose itself and spread. Pushing the viral populations to such "crash error" estate is what these drugs are all about. There are already comercial drugs aiming at this effect, and its effects have been thoroughly tested in vitro.
Realize also that a normal population of millions of HIV virions have a huge percentage of those virions inactive. This is caused by the crash error effect: too many bad copies. With this strategy, the virus accomplishes two things: it explores the maximum possible range of mutations, so that it looks forever different to the immune system, and it saturates the immune system with defective virions and viral antigens, diverging resources and allowing for a very tiny subset (don't recall numbers, but was well under 0.01%) to escape detection.
Another key concept is the synergy of viral particles. Many of those non-crashed virions are actually only partially crashed. When they coinfect a cell, betwen both virions they have enough good proteins that they can survive; i.e. reproduce and spread. Considering the cell infection rate is extremely low compared to the viral load in blood, and the even more extremely low probability of coinfection of two complementary virions, realize that was the number of ineffective virions be increased by a tiny amount, the virus would not be able to spread any further. By all means these drugs that push RNA viruses to the crash-error zone are a very good idea.