I can confirm that this is what happens: i.e. when "on profile" is set to NO, the field is not displayed on the profile except when it is being edited. I would have thought that NO should mean NO for both display and edit, but I don't see this as significant and can accept you leaving it along: you've got better things to work on I'm sure
Personally I prefer it not to show for edits as well so will continue to use my 'fix' mentioned earlier.