https://www.thelancet.com/journals/lancet/article/PIIS0140-6...
Edit: right, I'm also assuming the possibility of provirus mutation before this chain of events, and I don't think anyone can deny at least the mutation of HIV before it becomes a provirus.
Until then, I'll take the word of public health practitioners who've been steeped in the field for their entire careers. Their work has been significant enough to be published in Lancet which is a pretty good signal to this layman (though with a bachelor's of science in an unrelated scientific field, so no stranger to reading primary literature).
I think "can't" deserves at least something physically (as in physics) unlikely, not something that's been demonstrated in a DNA virus previously (and like I said, HIV in provirus form is not unlike a DNA virus).
i've no opinion on the topic at hand, but I would urge you to find a plethora of signals to form your opinions.
The Lancet has been responsible for quite a few negative 'public health' trends.
The Lancet is responsible, at least partially, for the whole 'vaccines == autism' thing of Andrew Wakefield's; and even ignoring that they have a history of poor review and retraction of work that ends up either being entirely wrong, or guilty of experimental misconduct.
In 1992 they published stuff that suggested a causal link between HIV infection and the oral polio vaccines.
In 1998 they published a (big tobacco funded) peper indicating that second hand smoke doesn't have as much risk as earlier thought.
In 2000 they published a study that claimed that St Johns Wort was as effective an anti-depressant as conventional SSRIs and TCAs.
Just because something has become 'prestigious' doesn't mean it should be trusted wholeheartedly.