Well, some vaccines are therapeutic in nature, where it's beneficial to take it while you have symptoms. Some vaccines are only helpful before you get a symptom, for example rabies.
I guess the above made it sound like there definitely can't be a therapeutic vaccine. But unclear about a preventative vaccine.
Their point is AIDS is the syndrome you get after it is too late and your immune system no longer works. The vaccine would be for Human Immunodeficiency Virus
It's more like saying "I miiiiiight be able to cure cancer, that's a bit tough and would require a lot of luck... I definitely can't cure death though."
There are some experimental cures that do seem to work at least in rats. But yeah there's no vaccine you just have to get sick and then get the cure and hope it works.