In my opinion, the biggest increase in moisture inside the pack is caused by the escaping vapors or liquid from the swollen cells when they get extremely hot.
Example: This summer I took my Victory on a trip 100km from home. I left with a fully charged battery, once on the way I charged it to about 80% and at the end I charged the battery to 75%. The last charge was around noon, it was very hot and the battery was heated to about 35 degrees Celsius. Then I parked the bike in the shade for about 5 hours. I then drove home, again with one charge on the way and one at home. When I then analyzed the data, I found that the humidity in module 5 had risen from 61% to 64% during the five hours of parking! It was completely dry and hot all day, so moisture from the surroundings was out of the question.