The instructor reported that a normal approach was flown, with the student as the handling pilot. The aircraft was subsequently flared normally but was not held off, descending onto the runway in a level attitude and touching down on its three wheels simultaneously. The nose of the aircraft continued to lower onto the runway until the propeller struck the ground. The operator subsequently reported that the lugs on the nose gear upper housing, which retain the hinge pin for the lower fork assembly, had failed. The nosewheel, complete with its fork assembly, had separated from the nose leg. There was no evidence of any pre-existing defects with the leg. The instructor reported that the landing did not appear to have contributed to the failure. The reason for the failure was not determined.