This article was published on 14 July, so it's a month old.

Perhaps the two last paragraphs are the most interesting.  They
include:

"The study's results also suggest that CD4 counts ... is an imperfect
measure of immune function."

And:

"...previous studies have shown a poor association between CD4 counts
at the point when a patient is diagnosed with AIDS and cancer rates,
suggesting other immune systems are more important."

What isn't clear from the article is whether the patients diagnosed
HIV+ had taken, or were taking, HIV medication.

However one of the study's conclusions is that it may be necessary for
HIV+ patients to begin ARV treatment earlier.  The, so called, "hit
hard, hit early" method of treating HIV has already been tried and was
a failure.  It killed patients and, perhaps, is the reason why so many
HIV drugs are now failing due to 'resistance.'

<http://www.theaustralian.news.com.au/story/0,25197,22069500-23289,00.html>:
"HAVING HIV increases the risk of developing 20 different types of
cancer - not just the three types that have been associated with the
virus to date, according to Australian research.

[...]

The study, by professionals from the University of NSW, reviewed the
results of 12 previous trials. Seven of those looked at cancer rates
in a total of nearly half a million patients with HIV, while the five
other studies examined cancer rates in 31,977 kidney transplant
recipients.

Transplant recipients have to take drugs that suppress the immune
system to prevent their bodies rejecting the transplanted organ, while
people infected with HIV also have impaired immune function as a
result of their infection, as the HIV virus particularly targets
immune cells.
[...]

'We believe that the striking similarity in patterns of increased
cancer risk that we have shown indicates that immune deficiency is the
probable explanation for the increased cancer risk,' they wrote. 'The
increased rates of cancers we have found ... suggests a broader than
previously appreciated role for the immune system in the prevention of
cancers related to infection. If immune deficiency is associated with
such a broad range of cancer types, then cancer is likely to become an
increasingly important cause of morbidity in people with HIV/AIDS.'

[...]

Cancers that affected both groups at higher rates included Hodgkin's
lymphoma - associated with the Epstein Barr virus - which is 11 times
more likely in HIV-infected patients than in the general population,
and four times more likely in transplant patients.

A range of other cancers associated with the human papillomavirus,
such as cervical cancer, and cancers of the mouth, penis and anus,
were also significantly more common across both groups.

'In other cancers, which are not linked with viruses, such as breast
and prostate cancer, both groups had similar rates to the general
population,' Professor Grulich said. 'This evidence suggests that
immune deficiency is associated with risk of cancer, and this suggests
we need to maintain people's immune systems at a higher level. That
might mean putting HIV patients on anti-retroviral drugs earlier than
is currently the case.'

The study's results also suggest that CD4 counts - a measure of how
many of one type of immune cell targeted by HIV are circulating in a
patient's blood - is an imperfect measure of immune function.

CD4 counts are often used to gauge effectiveness of anti-HIV therapy,
and when an infected patient should start using it. But previous
studies have shown a poor association between CD4 counts at the point
when a patient is diagnosed with AIDS and cancer rates, suggesting
other immune systems are more important."