I mentioned this. Due to a lot of issues I've never been physically diagnosed with coeliac but my Mum is and I get a lot from her and have all the same symptoms. When I'm in a more stable place in my life (only been saying that 4 years now) I will get tested but it means I have to eat gluten for 6 months which is agony for me. I do get a lot of tit for not being a 'real coeliac' though and I don't think people like Sarah help that... Although I do feel a bit like her as I'm undiagnosed.
Anyways, my Mum can't eat oats. There are gluten free oats (at least here) but I can sometimes react to them so I try avoid (never eat them anyway) but we definitely can't eat normal oats. I'm not sure in Aus but here oats are always bolded as an allergen and anything that says GF specifies that they are gluten free oats and if not, it's not gluten free. I don't think she can advertise something as suitable for Gluten free eaters (intolerance, choice or coeliac) if it has oats in, definitely not morally but that probably won't be an issue ha.
Sorry I replied before I saw your post. This is insane. So they're not gluten free they're just 'made' in a seperate factory/area? That's appalling honestly, I don't think you would get away with that here.