Often when people are shallowly honest, they still choose what true things they say in a kind of locally act-consequentialist way, to try to bring about some outcome. If you think someone is being merely shallowly honest, you can only shallowly trust them.
Deep honesty is the opposite of managing the other party’s reactions for them. Deep honesty means explaining what you actually believe, rather than trying to persuade others of some course of action.