No, it's nothing like HIV. HIV is a statistical thing: It's random chance if an infective particle travels.
A nuclear bomb like this is deterministic. Based on the distance, altitude, size (power), and type (fission, fusion, specifics of the design - especially the tamper) of the bomb you can calculate exactly what and how dangerous the effects will be.
The military was trying to show that they are able to make these calculations correctly, and that used appropriately, this type of bomb an be used without undesired damage.
It didn't work for them though, because people have an irrational fear of anything nuclear and are not interesting in hearing about any calculations.
It's one of those paradoxes similar to how people are completely unable to correctly calculate how risky an action will be. For example people are scared of flying but not crossing the street (a common event comes to be seen as less risky) or driving a car (if you are in control it seems less risky).
> It's amazing how these men have went on to live such long lives.
No, actually it was completely expected. If you can manage to internalize this, and actually believe inside your head that these men were quite safe then you will have gone a long way toward conquering an irrational fear.
PS. You may be thinking of Cancer when comparing to HIV which is indeed a random thing.