From personal experience, I had a red 50's UNC. Lincoln cent I had just pulled from a roll. I inadvertently touched the clear part of the 2X2 flip and left a finger print which transfered to the coin after placing it in. Tuff lesson but I did soak that coin in acetone immediately and it did remove the print.
Thanks DATA I didn't know very much about these coins. It goes alot deeper than I thought, and there could be unknown examples out there. It is possible. But you can bet there alot of fakes.