It's also worth pointing out, that if you put a "clean" blade (no oil or any other sealant, or insufficient sealant) into, or on top of, something that is made of fabric or paper, it will accelerate rust.
A good example would be the cheaper swords you can get online, that come with leather-only scabbards. If you don't oil it, and then just leave it in the scabbard, it will rust quite quickly. Same thing for leaving them on carpet. Fabrics and bare, rough leather will tend to draw moisture from the air and trap it on the surface of the blade.
If the blade is oiled properly before putting it into a scabbard, it will do fine. Over time, oil will also transfer to the scabbard interior and help protect the sword in the future. Scabbards with a wool interior will also help in this regard, because the wool contains natural oils.