As someone who taught a college, that's a flawed statement. Let me propose this to you. You teach Calculus 1000 and there is an end of term exam. Your normal end of term exam is one where everyone sits in the same room, proctors are looking for cheats, things checked, etc. Instead this year you tell your students that this year it will be a take home exam with the following rules: 1) they have 2 hours to do it during the team home peroid; 2) no cheating by the honor system.
Do you think the rate of cheating will be the same? I mean by your logic, it should be.