You probably aren't doing anything wrong - it depends on the density of the cake, quality and oiliness of the paper liner. I use commercial paper liners which most bakeries would use. They are a little heavier and have a bit of a sheen on the inside. Also, the fresher the cake, the softer it is, with more likelyhood to crumb when the wrapper is removed. Try putting them in the fridge an hour or so and see if that helps (using your regular cases - but don't oil them, it won't help and will just make it messier).
"Variety is not just the spice of life, it is the key to life" - Chef Michael Smith