It actually gets to a really interesting question as to "what counts as infected?"

If there's latent proviral inserts that never activate and propagate, to the point that they're ubiquitous in the DNA of the host, then it strains the definition a bit in most contexts. If you're doing genomics then for those purposes it makes sense to call it an infection. If you're doing something at the level of epidemiology, then probably not.

Having a bunch of boundary cases in definitions is pretty much a staple for biology though, so it's not worth losing any sleep over.