RytheStunner is correct, your new lungs have the DNA of the donor, and since the donor does not have CF, the lungs you get have 2 normal, functional copies of the CF gene. Thus, your new lungs do not have CF.
However, since the lungs were the only things transplanted, the rest of your body would still have CF...you still may have malabsorption issues, your sweat would still be salty, etc. In addition, if you were looking to have kids, your sperm or eggs would have your mutated CF gene, so you could still pass the gene on.
Thus, I think that what you were told is that since CF is genetic, after a lung transplant you'd still have the symptoms of CF in your non-lung organs (GI, sweat, reproductive). But your new lungs themselves would not have CF.
Hope this helps.