Well, what I posted is correct. If you'd like to examine the matter further, there are two areas to look at:
1) Chemical potential, or "Activity," and equilibrium. Namely, at equilibrium (where there is no mass transfer with time between phases or species) the chemical potential or "activity" is identical on each side. The activity of a crystal form is 1; the activity of the saturated solution is 1. A saturated solution exists when a solid phase is in equilibrium with a dissolved phase.
If in fact the chemical potential or "activity" of the solution is LESS than saturated, then what happens is solid dissolves back into the liquid. It's not at equilibrium.
I don't want to do Google searches on possible physical chemistry course webpages that may discuss this as another person could find it as rapidly as I could I would think, but most assuredly the above matters are thoroughly treated and can be found with keywords from what I wrote above.
2) Experiment. One will find that whenever a solid in a liquid has reached a steady-state point -- it's neither dissolving further into the liquid nor precipitating out more -- that a measurement of the dissolved amount will find it to be saturated.
3) Definition. I expect one can find definitions of a saturated solution that make plain that this is a solution of a concentration which is in equilibrium with the solid phase of the same material.
Anyway, it just isn't the case that everything is pulled out. If the oil were less than saturated, then the crystals would dissolve back into the oil until it was saturated. But they are not going to keep precipitating out when the solution becomes less than saturated: precipitation occurs only when supersaturated. Though (at constant temperature) it isn't the case that a less-than-saturated solution ever results from precipitation, anyway. (Definition of saturated solution.)