[Lack of] electronic interference notwithstanding, it appears that ACTUAL interference with the Captain's duties is a REAL issue in PA-32's airplane (and any other small airplane where the pax are not separated from the Captain). The noise distracted him from his duties at a critical time -- during the takeoff roll. It was enough of a distraction to cause him to take action. It could have distracted him from a warning light or other sign of malfunction, or caused him to miss an ATC transmission.
If I were PA-32, I would have taxied back to the ramp and unloaded that passenger. She IN FACT caused a significant distraction that had an adverse safety impact. That may be the ONLY way to get the message through her thick skull!