Have you ever tried it? Give it a try. Try handling duct tape with latex gloves on ---- oh, what a sticky jumbled-up mess you get into! Chances are better there are prints.
I wonder if have a different kind of duct-tape here in Australia...
The stuff I am thinking of is silver on the non-sticky side and has like a kind of gummy glue-ish type adhesive on the otherside? Plumbers, carpenters etc use it frequently. Not easy to use with glove but not impossible. Workmen have to wear gloves on worksites and dont always remove them while working with what we call duct-tape...
ETA- I PRAY you are right and she put her grimey mitts all over the tape.