Why does paper go translucent when wet or if it comes in contact with vegetable oil?

Paper is a white opaque color because the fibers of the paper scatter the light back. Oil fills the spaces and kills the scatter, transmitting the light through itself so that it becomes more or less translucent.Why does paper go translucent when wet or if it comes in contact with vegetable oil?
Paper is already translucent. Making it wet just increases the translucency. Why does it become more translucent? My guess is that any liquid makes paper thinner.