I'm talking about the kind that is a leather case with the thin wood interior. I heard that it should be wiped down with distilled water, is that true? Probably a silly question, but I figure I'd ask anyway.

If you are talking about a 2,3 or 4 cigar case for a day or so, the answer is no.

If you are talking about a larger case for over 5 cigars I would think you should also have wither a small Boveda pack or some other cigar humidification device.

I have a 36 cigar SHERMAN, a hard plastic case with foam shelves. I has a digital hygrometer/thermometer and a humidification device, but since the case is plastic, it does not breathe and I have found it can overhumidify my cigars.
I take it on vacation when I am going to be away for over a week.

I also have a Czonka Survivor that holds 4 cigars. It has 2 small clay humidification devices and 2 little bottles for distilled water. This one is for 1 or 2 day excursions.

Thanks Doc