Yeah this is my understanding too. Quaker Oats for example wrote: "Yes, oats are naturally gluten-free. However, during farming, transportation and storage, gluten-containing grains like wheat, rye, barley and spelt may be unintentionally introduced."

Just like Sweden, in North America you can buy gluten free oatmeal that's made specifically to not include cross contaminates.

For the most part cross-contamination is the major issue, but it’s a bit more complex than that. Oat proteins are similar to the giladins in wheat that trigger coeliac disease. Certain oat cultivars are more similar than others. This means that some varieties of oats and some coeliac sufferers are not compatible. I can’t eat oats.

Originally oats were considered gluten containing until a new more sensitive enzyme-based gluten test was developed which does not trigger for non-contaminated oars. Unfortunately enzymes aren’t how coeliac disease works.