You were doing pretty well right up until you mentioned gluten. This near fanaticism with avoiding gluten is approaching the same level of thinking organic foods are more nutritious.
Gluten comes from certain grains. Despite this fact, I have seen products, including fruit itself, labeled as "gluten free" which do not use grain in their production. This article spells it out very nicely:
The researchers noted that many symptoms attributed to gluten may actually be caused by sensitivity to other components of wheat flour or other ingredients found in wheat-based foods like bread, pasta, and breakfast cereals.
Symptoms that have been attributed to gluten sensitivity include diarrhea, abdominal cramping, bloating, headaches, fatigue, and even those associated with attention deficit hyperactivity disorder (ADHD).
Di Sabatino and Corazza write that some people may experience these symptoms when they eat foods containing gluten simply because they believe these foods will make them sick.
They conclude that common sense must prevail to "prevent a gluten preoccupation from evolving into the conviction that gluten is toxic for most of the population."