Sensei is indirectly quoting from Shinran Shonin's own words on how Shin Buddhists view Amida Buddha.
"One Vehicle" here refers to the Primal Vow. "Perfect" means that the Primal Vow is full of all merits and roots of good, lacking none, and further, that it is free and unrestricted. "Unhindered" means that it cannot be obstructed or destroyed by blind passion and karmic evil. "True and real virtue" is the Name. Since the wondrous principle of true reality or suchness has reached its perfection in the Primal Vow, this Vow is likened to a great treasure ocean. True reality-suchness is the supreme great nirvana. Nirvana is dharma-nature. Dharma-nature is Tathagata. With the words, "treasure ocean," the Buddha's nondiscriminating, unobstructed, and nonexclusive guidance of all sentient beings is likened to the all-embracing waters of the great ocean.
From this treasure ocean of oneness form was manifested, taking the name of Bodhisattva Dharmakara, who, through establishing the unhindered Vow as the cause, became Amida Buddha. For this reason Amida is the "Tathagata of fulfilled body." Amida has been called "Buddha of unhindered light filling the ten quarters." This Tathagata is also known as Namu-fukashigiko-butsu (Namu-Buddha of inconceivable light) and is the "dharma-body as compassionate means." "Compassionate means" refers to manifesting form, revealing a name, and making itself known to sentient beings. It refers to Amida Buddha. This Tathagata is light. Light is none other than wisdom; wisdom is the form of light. Wisdom is, in addition, formless; hence this Tathagata is the Buddha of inconceivable light. This Tathagata fills the countless worlds in the ten quarters, and so is called "Buddha of boundless light." Further, Bodhisattva Vasubandhu has given the name, "Tathagata of unhindered light filling the ten quarters."
Notes on Once-calling and Many-calling http://www.shinranworks.com/commentaries/onceandmany2.htm
Nirvana has innumerable names. It is impossible to give them in detail; I will list only a few. Nirvana is called extinction of passions, the uncreated, peaceful happiness, eternal bliss, true reality, dharma-body, dharma-nature, suchness, oneness, and Buddha-nature. Buddha-nature is none other than Tathagata. This Tathagata pervades the countless worlds; it fills the hearts and minds of the ocean of all beings. Thus, plants, trees, and land all attain Buddhahood.
Since it is with this heart and mind of all sentient beings that they entrust themselves to the Vow of the dharma-body as compassionate means, this shinjin is none other than Buddha-nature. This Buddha-nature is dharma-nature. Dharma-nature is dharma-body. For this reason there are two kinds of dharma-body with regard to the Buddha. The first is called dharma-body as suchness and the second, dharma-body as compassionate means. Dharma-body as suchness has neither color nor form; thus, the mind cannot grasp it nor words describe it. From this oneness was manifested form, called dharma-body as compassionate means.
Taking this form, the Buddha announced the name Bhiksu Dharmakara and established the Forty-eight great Vows that surpass conceptual understanding. Among these Vows are the Primal Vow of immeasurable light and the universal Vow of immeasurable life, and to the form manifesting these two Vows Bodhisattva Vasubandhu gave the title, "Tathagata of unhindered light filling the ten quarters." This Tathagata has fulfilled the Vows, which are the cause of that Buddhahood, and thus is called "Tathagata of the fulfilled body." This is none other than Amida Tathagata.
"Fulfilled" means that the cause for enlightenment has been fulfilled. From the fulfilled body innumerable personified and accommodated bodies are manifested, radiating the unhindered light of wisdom throughout the countless worlds. Thus appearing in the form of light called "Tathagata of unhindered light filling the ten quarters," it is without color and without form; that is, it is identical with the dharma-body as suchness, dispelling the darkness of ignorance and unobstructed by karmic evil. For this reason it is called "unhindered light." "Unhindered" means that it is not obstructed by the karmic evil and blind passions of beings. Know, therefore, that Amida Buddha is light, and that light is the form taken by wisdom.
Notes on "Essentials of Faith Alone" http://www.shinranworks.com/commentaries/essentialnotes3.htm
Yes it's true none of the Shin texts put Amida in a historical context, because Amida goes BEYOND samsaric historical context. Using samsaric history or mythology, to describe Amida, to me at least, is futile and worthless.
It is taught that ten kalpas have now passed
Since Amida attained Buddhahood,
But he seems a Buddha more ancient
Than kalpas countless as particles.
Hymns on the Pure Land 55 http://www.shinranworks.com/hymns/jodowasan3.htm