Paper itself can cause unexpected toning of coins over a similar time period; it often contains sulfur. However, the damaging chemicals from degraded plastic can pass straight through paper, as well as through other kinds of plastic that would otherwise be quite safe.
Case in point: I was recently given an album of Australian decimal coins which were in mint state, or close to it, when they were placed in the album. The album has plastic pages, with thin cardboard pages to back them. In this particular case, the plastic album pages themselves weren't the problem - the coins in the pages in the middle of the album are still mint state, with no sign of PVC damage.
However, the coins in the front and back pages are now ruined, because the album cover is made of a different kind of plastic which has clearly degraded - it feels sticky to the touch. The 50 cent coins (made of cupronickel) were on the front page, which was directly in contact with the covers, and every single one of them has turned a sickly green colour.
All of the one cent coins, on the back page, have also been ruined, turning a shocking black-brown colour, even though the 1 cent page was protected from direct contact with the album cover by the backing sheet. The only explanation for all the bronze 1 cent coins discolouring in the exact same fashion is that the reactive agents migrated straight through the backing sheet, into the album page and onto the coins.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis