Like GPS System? The acronym takes on a life of it's own as a 'word'.

Is GPS System common? That looks and sounds weird to me.

Sure, I've heard it said more than seen it written. Especially on news stories: "the car was tracked using the GPS system", etc.

To most people, HIV is a disease. What's the more elegant alternative?

I hear a lot of people call it "The HI virus".

The most acceptable way may not be the most correct, but to correct it is more effort than it's worth.