The issue is not "has there been a study that shows mobile phone interfere with an aircraft...?"
Your question should be, "Has there been a study that shows mobile phones do NOT interfere with an aircraft's ... equipment?"
There is ample evidence that there has been some interference at various times. A cursory search of these fora will reveal that.
I believe that there have been trials overseas with mobiles in flight - using retransmitting equipment on the aircraft. Trying to explain this concept to the average JQ passenger would not be easy.
And yes, the other issue is willful disregard for the authority of the crew.