It's not even possible to make commercial truffle oil with real truffles, because the flavor doesn't last longer than a day or two. You could theoretically make it in your house and then use it immediately, but there wouldn't really be any point.
Actually, the reason it's not possible to make real truffle oil is because (drum roll plz) truffles aren't soluble in oil. Or rather, the compound that holds the truffle essance is not soluble in oil.
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.