All non-organic soils can be compacted. Organic soils rot, so they are right out.
Here is the thing about soils. It is not about spraying them with a hose, and "packing them real good". Soils have a maximum dry density, where they will not compact (settle) any further. Every soil has a different maximum dry density. They only way to know this value, is to test it - normally with a standard proctor test. It is not a hard test to perform, nor does it require a lot of fancy equipment (I have performed 100's of them in the field). Then you have to know if you have compacted it enough. To do that, you need to calculate moisture/density curves for the soil, make sure your soil moisture is within the correct range, compact it, and then test the compacted soil - either with an Ottawa Sand Cone or a Nuclear Soil Densometer. You can buy a sand cone, you are not buying (or transporting) a densometer. Then if you have loose, non-cohesive, soil it can wash out. I could get into how to calculate slope stability of both a free standing soil and a soil with vertical loading, but that is not necessary. I just highly doubt that anybody who puts fill for a pool on a grade cut is running those calculations either.
The moral of all of this is, the average homeowner (or for that matter contractor with a bobcat and plate compactor) does not have the knowledge or resources to know if they have compacted any fill enough. With a pool weighing multiple tons on top of it, any soil that is not compacted enough will eventually settle - with disastrous results. This is why it is recommended to not use any fill. What is there already has had plenty of time, moisture, and surcharge on it to compact on its own.