As we know from Haiti, if you make sure people get good nutritian and regular checks (not necessarily from doctors or nurses!) to make sure they're taking their meds and that nothing untoward is happening it reduces the death rate substantially. I've never heard that Cuba's health system was anything to write home about, but if (as seems probable) it can supply the really elementary care required, that helps a great deal.
But in the body of the story you find a few of the reasons Cuba has low death rates from Aids.
It has one of the world's very lowest infection rates. That is for a combination of reasons.
One is that when HIV was first discovered in the mid-80s Cuba controversially quarantined those it found to be carrying it.
The Communist-led island also has the advantage of a good public health system and a largely non-traveling, non-drug injecting population.
It is now offering its expertise in Aids prevention and treatment to its neighbours.
As I said earlier, a good public health system isn't necessary, just an adequate one. But a low death rate from Aids comes from a low infection rate, and the low infection rate comes from isolation. Quarantine was a good idea: it helped nip the spread in the bud. Frankly, in the early Aids years, before we understood how it was transmitted, we should have been doing that too. Public health officials were political cowards. And a non-traveling population (a polite way of saying that they are trapped in a police state) isn't going to have much opportunity to get infected elsewhere.
But neither quarantine nor restricting travel nor eliminating IV drug abuse are really the domain of doctors and nurses, so all this training will do (assuming it does anything at all) is slightly lengthen the sufferer's lives, not reduce the number of patients. A good thing, but prevention is better. And Cuba's prevention policy isn't perfectly applicable elsewhere.