I would guess that it's quite difficult to guarantee a beer as wheat-free if wheat is ever used at the brewery. You definitely couldn't do it on tap because the brewer has no control over what's in the lines. 9 White Deer's Kölsch, for example, is sold as gluten-free Stag Saor when bottled but the same beer is called Fia on draught, with no gluten-free statement, because the brewer can't guarantee it.
Totally agree on the ingredients listing, btw, and it's a pillar of Beoir's campaign. As well as no ingredients, there are beers with inaccurate ingredients listing out there too "Vanilla and Oatmeal Porter. Ingredients: Water, Barley, Hops, Yeast." Ah here...
Incidentally, I think the 9 White Deer Stag Saor IPA is really good, if you're looking for one that deffo won't have wheat in it.