For the record, only the part that I bolded is from Shelley Case. She does not make an exception for smoke. The person claiming that smoke is an exception is not Shelley Case.
I also found this other site (also not a scientific, medical source):
As Shelley Case, an international gluten-free expert writes "barley malt extract or barley malt flavoring is almost always declared as "barley malt extract" or "barley malt flavoring". For this reason, most experts do not restrict natural and artificial flavorings in a gluten free diet"2 A notable exception to this rule is "smoke flavor", which often contains barley flour.3
Smoke flavoring is listed here on our list of safe ingredients.