You could recommend some experimentation to locate the source of the humidity.
"He taped plastic to to the basement floor and it remained dry."
My first experiment (after the above) would be to do the same to the basement walls. If moisture is coming in the walls (were not sealed properly, or maybe not at all), then that is the problem. It may be one wall, or one section of one wall.
After that, you could try other things: Do they have a fireplace they could use for heat while shutting down the heating system (although I doubt the heating system is a problem, but the intent is to isolate non-problem items from the list), then start with other equipment, exhaust fans, etc. Maybe they have too large of exhaust fans and are pulling a negative pressure on the house, which is in turn sucking air (and moisture) from wherever it can.
Maybe installing this would allow them to pressurize the house without using unduly cold outside air to do so. See if one can be rented and install it through a window at the basement.
Air-to-air heat exchanger
An air-to-air heat exchanger mechanically ventilates and dehumidifies homes in colder climates. During the winter it transfers heat from the air being exhausted, to the fresh, outside air entering the home. Fifty to eighty percent of the heat normally lost in exhausted air is returned to the house. Air-to-air heat exchangers can be installed as part of a central heating and cooling system or in walls or windows. Wall and window-mounted units resemble air conditioners and will ventilate one room or area. They are easy to install.