Sorta hard to know what is meant by "lightly oiled".
Varies with the oiler, seems to me.
Anyhow, I've always followed my uncle's advice: "As near to dry as you can."
So, after the last dry patch is run through in cleaning, I spray very little RemOil on a patch and run it through. Call it a "miniscule film", I guess. Anyhow, I've had no trouble with first-shot flyers.
Absent really wet weather, I've rarely cleaned a rifle during the two-month Texas deer hunting season. Never had any rust problems. Basically a dry bore after checking my sight-in ahead of the season.