Why are plastics lipophilic?
First, many plastics are somewhat porous. Since plastics are permeable to water vapor and oxygen, coffee and other food products are sometimes packed in two-layer bags of polyethylene (for strength) laminated to aluminum foil (to reduce permeability).

Second, lipids and other non-polar substances can dissolve in and and migrate through common plastics used in food containers, such as polyethylene and polypropylene, as you and @Alchimista note. This is why carotene, lycopene and other chemicals in tomatoes eventually stain poly containers permanently: they've dissolved into the plastic.

In a similar way, mercury dissolves into gold (e.g. jewelry) in a matter of seconds, leaving a silvery stain. That stain then disappears in a week or two as the mercury migrates throughout the object.

The reverse phenomena also occurs, where substances in plastic packaging can migrate out of the packaging.

As the Bard might have put it, "Will all the water in the ocean wash this food from my cans?"