Oil is not water-soluble, and vacuuming does nothing
The soil in a traffic lane on a carpet is mostly dry particulate that a vacuum can lift. The soil on a sofa arm is largely sebum — the oil skin produces continuously — mixed with hair product, hand lotion and whatever transfers from clothing. None of that responds to suction, and none of it dissolves in plain water. A general spray-and-extract pass across the whole sofa lifts the loose surface soil and leaves the oil sitting exactly where it was, which is why a cleaned sofa can look better overall while the arms still read as darker than the rest of the piece.