During a VOR/DME approach the airplane broke out of clouds about 750 feet above ground level and made a normal touchdown. Winds were 330 degrees at 5 knots. The flight crew reported that the runway was wet, but there was no standing water. The pilot engaged the nose wheel steering just below 60 knots indicated, and the airplane started into an abrupt left turn. Right rudder input had no effect, and the airplane turned 180 degrees, and slid backwards down the runway before it departed the left side of the pavement. The right main landing gear collapsed after sinking into the soft mud. The airplane sustained substantial damage to the right wing tip, right wing aileron, right engine propeller, right main landing gear, and the right side of the fuselage was wrinkled and deformed. Examination of the nose gear steering system, hydraulics, brakes, and rudder system by an FAA airworthiness inspector and Piaggio America, Inc., personnel found no mechanical anomalies. The Pilot's Operating Handbook (POH) paragraph 4.2.13, the airplane check list, as well as Flight Safety International Training Manual, all state that "Steering engagement during landing is prohibited." The FAA Inspector interviewed the flight crew, Flight Safety International personnel, and Piaggio America, Inc., training personnel. The FAA inspector reported that the POH requires that the nose wheel steering be disengaged at or before 60 knots during the takeoff. Also, the rudder becomes ineffective below 40 knots. During the interview with the pilots, they said they were unaware of the prohibition against engaging the nose wheel steering during landing. They further observed that because the steering system is used up to 60 knots during takeoff, they assumed that the nose gear steering was to be engaged after touchdown during the landing rollout, while slowing through 60 knots.