Perhaps, but you can use opponent targeting effects like Duress on yourself and successfully take your own cards, so I don't see how this is any different. Someone else tried this out 1v1 and it didn't work for them, I just tried it solitaire and figured it should still exile it.
Match: 268052168
Game ID: 875510392
Cast a morph, attempted to exile with Deputy of Detention, no prompt to exile permanent came up and permanent didn't exile.