Mostly what TwoDDs said but my wheat allergic child seems to have much lower thresholds across the board when compared to others who share same allergens if that makes sense. Tolerance for wheat is higher than milk in same child, but compared to other children with same allergens eliciting doses are much lower and instances of anaphylactic reactions requiring epinephrine are greater.

The form factor during encounter seems to matter. It's more often we come across large amounts of powdered wheat, barley with much smaller amounts of powdered milk a close second.

Gluten free labeling doesn't mean much in USA if you count on it blindly for two reasons (1) the demand for gluten free items driving marketing for such products is lifestyle choice under general health promotion (2) some labeled gluten free have caveat messages directed at individuals with celiac should not consume due to gross contamination.

Celery is one of the regulated allergens in the EU, along with lupin: 
http://www.foodallergens.info/Legal/Labelling/FoodList.html

I, too, wonder how people were selected or excluded from this study. Considering contact ingestion is a problem for several people on this forum, at extremely low levels, I often wonder if this could make food labels even more difficult to navigate.

How do people with wheat allergy fare with the current gluten-free testing and labelling?  Has anyone had reactions below that threshold? Then again, thresholds for wheat seem to be higher than some other allergens, or at least with people I know.  Too many questions...

I'd love to know what the exclusion criteria were.  This sort of thing is really a great, and much-needed study topic.  BUT-- most often, such studies can only get IRB approvals when the exclusion criteria are set up to exclude those people who are likely to have lower thresholds.

Lowest thresholds tends to also = most severe reaction history, though, which is why they get excluded from studies with challenges.     Of course, even when the study isn't set up that way-- they tend to self-select out of the study cohort.  So.