Is a stronger statement that hepatitis C is NOT curable, as it's a retroviral infection, thereby rewriting host DNA? [ Edit: i'd remembered incorrectly from decades ago: it's an RNA virus ]
And HPV wasn't linked with cervical cancer yet - that doesn't mean it wasn't a disease. And I'm comfortable calling HSV-2 a disease based on the potential congenital consequences alone.
It's certainly a manageable one, and the stigma around it is silly, but if the common cold is a disease, then herpes is.