Better to leave it dirty than to damage it further. Call them crazy. If your board is in fairly good condition, all that is necessary is an occasional wipe with a soft cloth. Keep it in the original box, or if that is not available, a relatively sturdy box the same size. Store it in a clean dry place.
Closets are fine, damp garages are a no-no.
This hermetically seals them from the elements and is the best protection. The cost of shrink-wrapping equipment is a little over the top for most people, so we recommend securely packing your boards in plastic bags if you are planning to store them for long periods. Always test clean a small area of the board first. Keep scrubbing to a minimum and be alert for any damage. General Cleaning Glass cleaner like Windex or Glass Plus works wonders on many dirty boards.