It IS possible to have CF and for genetics testing to not identify one or both genes. Obviously would be EXTREMELY rare to not be able to identidy either!
I have CF...most of the classic symptoms, positive sweat tests and yet so far only 1 mutation identified...DF508. My 2nd is yet to be identified yet noone questions my CF diagnosis! I def have it, I just have a rare mutation. I do have to say I was diagnosed and gene tested before Ambry and Quest's full panel DNA testing came out. And due to insurance issues(like no insurance!) I haven't been tested through them so its entirely possible my 2nd one could be identified now.
Generally a CF diagnosis is made from a combo of things....Clinical symptoms, sweat test, DNA testing and in harder to diagnose cases NPD testing