We had to stop buying oatmeal, as it is often cross contaminated with wheat and our daughter is wheat allergic.  And there is often no wheat warning on oatmeal packaging even though I think all oatmeal is 'may contain wheat', so oatmeal is off limits to us

ie: Healthy Times cereals have wheat cross contamination even though it is not labelled - in Canada, the government forced the company  to add a 'may contain wheat' on their rice cereal as they found wheat/gluten in it when testing samples and there was no warning on the label (our daughter had 2 reactions to Healthy Times and we sent the box and its contents to the government as they tested it - Canadian Food Inspection Agency).. all the product was pulled off store shelves by order of the government until the warning label was added to the product)

I think that's actually been true of them for a long time, Jessica.  I seem to recall that from the old old place, and it't a reason why we quit using teh Corn squares cereal from them way, way, WAY back.... which would have been when DD was still allergic to wheat and soy, so about nine, ten years now.

We do use Quaker quick and instant oats in the big canisters.  But for just eating, we like Snoqualmie Falls Lodge, but that's because we're oatmeal snobs.  Scots ancestry.   

I looked all over and can't find that thread about Quaker. Maybe it was a dream.

Someone posted recently that they called Quaker and were told that advisory labeling would only be used if they thought there was a risk, not necessarily for all shared lines. Right now we're using Great Value brand plain oatmeal and Better Oats brand for instant. Better Oats does not label for shared lines but at this time, they don't make anything with nuts. If they ever do we'll quit using them.

I remember from somewhere that Quaker uses a 'may contain' statement if anything is on shared equipment. I've always trusted their labels, no pn/tn and I eat it. That includes their flavored oatmeal packets and canisters of whole/rolled/instant/multigrain oats.

From their product FAQ for snack bars, it looks like they still label shared equipment with 'may contain' and their labeling can be trusted:
All Quaker® Snack Bar packaging includes the warning that the product "may contain traces of peanuts." Specifically, the following Quaker Snack Bar varieties contain peanuts or peanut butter — Quaker Chewy® Peanut Butter Chocolate Chip Granola Bars, Quaker Chewy® Peanut Butter Chocolate Chip Granola Bars with 25% Less Sugar, Quaker Chewy® 90 Calorie Peanut Butter Granola Bars, Quaker Chewy® Dipps® Peanut Butter Granola Bars, and Quaker® Granola Bites – Peanut Butter. The warning does not mean that peanuts are added to any other varieties; there have been no product reformulations. Federal laws regarding the use and labeling of all ingredients are followed carefully by the Quaker Oats Company.

Between the production of flavors that contain peanuts or tree nuts and those that do not contain these ingredients, the line is shut down and thoroughly cleaned. Due to the complexity of some of the equipment, it may be difficult to clean some areas completely. Trace amounts of peanuts and/or tree nuts may be left behind in these hard to reach areas. Because we realize the seriousness of food allergies and because we are concerned about the health of our consumers, we feel it is our obligation to warn consumers about the possibility of trace amounts of peanuts or tree nuts since other products share production lines. For complete nutrition and ingredient information for all Quaker® Snack Bar products, please visit our products section.

What oatmeal do you use?  I'm sure the Quaker variety packs are out, what about the big red canister of Quaker?