>What is the difference between giving them a password which wipes the phone and giving them a password which opens a blank phone?

They don't get any indication that there was data there to be deleted, and you don't just factory reset but flash w an image of a clean phone that's been used. It has apps, it has accounts, it looks to the untrained eye (because that's who's looking at it) like a phone that was used normally by someone who has done nothing wrong.