Facit doesn't mention aniline for this issue, but these particular coils are found on three types of paper (simplified categories) and one is "clean white, translucent" and another is "faintly rose-tinted, thinner, sharply translucent." I think the translucence is the effect you are seeing here.
The third paper choice is "faintly rose-tinted, thick" so I suppose that is possible.
I haven't associated translucent with oily. I have quite a bit of early Sweden. If I get a few spare minutes, perhaps I can scan the backs of some stamps. (I don't have scans of the backs ready to go...)
eta: I meant to say that if you have access to a UV lamp, you could see if there is an effect.
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