This is an interesting study. They concluded that the amount of gluten a celiac can tolerate before a harmful autoimmune reaction occurs varies greatly from one celiac to another. This is consistent with message we see from people with celiac disease.
They concluded that any celiac should probably be OK if they ingest less than 10mg of gluten per day, this is actually a larger number than I would have guessed.
Bottom line: you're still reading every label.