@Tealer, I am not able to find that sutta that you refer to. Maybe some user here will be able to find it.
Here is a description of the word vimutti:
Vimutti (Pāli, ‘freedom’, ‘release’, ‘deliverance’). Freedom from suffering (dukkha), the goal of the Buddhist path. Canonical Buddhism distinguishes two kinds: freedom through understanding (pañña-vimutti) and freedom of mind (ceto-vimutti). The former means final release from suffering, the ending of rebirth, nibbāna, and is so named because it is brought about by understanding (pañña) which develops out of the practice of insight meditation (vipassanā). The latter represents the qualified freedom from suffering which arises out of the practice of concentration meditation (samādhi), Ceto-vimutti can only become permanent and unshakeable (akuppa), synonymous with final release, if it is combined with paññāvimutti, that is, if the meditator cultivates insight as well as concentration.
From the above description, it would means that for a Ceto-vimutti it would need to be both way liberated (“ubhatobhāgavimutto“).