There are reasons why you can get a false positive, many of them are fairly uncommon diseases/syndromes though. I found this list online as part of an article at http://www.cysticfibrosismedicine.com/htmldocs/CFText/sweat.htm
<b>False-positive sweat test result</b>
Adrenal insufficiency, anorexia nervosa, atopic dermatitis, autonomic dysfunction, coeliac disease, ectodermal dysplasia, familial cholestasis (Byler's disease), fucosidosis, G6PD deficiency, glycogen storage disease type 1, hypogammaglobulinemia, hypoparathyroidism, hypothyroidism, Klinefelter's syndrome, malnutrition, mucopolysaccharidosis type 1, nephrogenic diabetes insipidus, nephrosis, pseudohypoaldosteronism, psychosocial problems (Rosenstein & Cutting, 1998, Duddy et al, 1987).
In an earlier post of your's I saw that you were going to Baystate Medical in Mass. which does have an accredited center. Just to clarify though, are you going to the CF center there or just going through a doctor that works there? It is important to be seen at the CF center itself and not just somewhere in the hospital. Don't know if that's the case with your child, but just wanted to throw that out there.
Also, my son was in the same boat as your child. He had numerous (too many to count) clearly positive sweat tests and no genetic mutations could be found. We ruled out all of the above other reasosn for a positive sweat test and now they have decided to officially call it Atypical CF.