Yesterday a guy in a flex wing called (no transponder) asking to transit overhead my airfield at alt 4000ft. I made no attempt to ascertain where he was, but informed him that the base of controlled airspace overhead was 3500ft, and at 4000 he would be in controlled airspace. He said that conflicted with his information, but he would check. He eventually reported transitting at 3000ft. I was very busy with other traffic, so I didn't have time to identify him on radar.