I don't have anything resembling "coils" in my freezer -- do you have a chest-type, or is it an upright freezer, Lyn? (Mine is a chest.) Mine does have a couple of baskets that hang from the top edge, though, which seem like they would be comparable to shelves, and they have never gotten any kind of frost buildup on them. It does kind of seem like oiling anything on the inside might just be kind of messy.
I really do consider it an easy job; the worst part is taking all the food out, but I usually do it before I start harvesting very much from the garden, and every now and then I need to get rid of a few things that have been hanging around too long anyway! Probably takes me 20-30 minutes altogether.
Never trust stuff you read online