Surely it doesn't need to be a solution - it can just be a suspension? The difference between extra virgin olive oil and purer grades are that the purer grades are filtered, not (e.g.) distilled.
Virgin means the oil comes from a mechanical process, not a chemical one.
The purest grade extra virgin olive oil is the first cold pressed. It's neither filtered nor distilled. Refined olive oil however is filtered and also tasteless.
I don't mean 'pure' in a good sense, just that it is a simple mixture.