As you said above: "The unexpired I-94 may protect him from accruing days towards 3/10 year bar though", that is because the person is lawfully present (or say "authorized presence") during the I-94 duration (unexpired) and thus, he is not subjected to 3-year or 10-year bar. - It would not appropriate to interpret "do not accrue unlawful presence" to "lawfully present"
-I think if a person presence is not counted as unlawful presence, it is reasonable to say this person's presence is lawful or say "authorized stay", and don't think there is a status between lawful/authorized presence and unlawful presence. Even if a person violate the condition and term of status during I-94 vadility, he is authorized to stay until USCIS/DHS or immigration judge make a decsion that he is not authorized to stay.
