Actually, independent of the whole low-carb craze, there's some evidence indicating that, as carbs go, wheat is a particularly bad one. Substantially worse than corn, rice, root vegetables, and other sources of starch.
People have definitely conflated the wheat gluten allergy issue (celiac disease and other forms) with low-carb dieting in general, which is misguided. As the article points out, the percentage of the population actually suffering from allergies to gluten is tiny. [1] But it may not be a bad idea to cut down on wheat, regardless. Especially products with highly processed wheat as a key ingredient.
[1] Although it may be growing, for reasons not currently understood. Alternatively, we may just be experiencing a boom in the diagnosis -- either a result of over-diagnosing, or rather, correct diagnoses after many decades of under-diagnosing.