Key word there is moist, not wet. The healthiest plants i've received came in slightly damp paper towels or newspaper. The ones that came with excess water at the bottom of the bag typically didn't fare as well, but most still survived.
I do damp (very well rung out) paper towels, in ziplock bags with just enough air to keep plants from being crushed. Then fill the gaps in the box with whatever I've got laying around, usually paper or some sort of insulation. Never had a complaint about plants not making it, even long trips.