I'm going to die on this hill that water is not inherently wet (and by extension oil is not inherently oily).

To say that something is wet, it needs two components: water and not water. You can say that a surface is wet because the water can be removed. If you remove water from water it's just less water. You can say that the container that the water is in is wet, but not of the water itself.

The same applies to oil as well.