I don't think there is anything to forgive. It's a sensible question. And this is a very interesting position to take, and not uncommon among those who are more inclined to follow the Theravada traditions.
Strictly speaking, that quote is accurate. One cannot overcome ignorance through offerings and prayers. But through making offerings (whether real or imagined) one can overcome greed, and through prayers one can overcome anger and hostility toward others. Actually, "prayers" is not a very good word, in my opinion. And indeed that word may have been acquired through translations in which terminology was borrowed from the Judeo-Christian tradition. "Aspirations" might be a better term. personally, I can't stand the term 'prayers'. It turns me off for the very reasons you mention. But this is not the fault of the Buddhist traditions. "Prayers" in Mahayana Buddhism are generally, a wish that all beings be free from suffering.
So, of the three poisons of ignorance, greed and aversion, making offerings and "prayers" or aspirations for the benefit of others addresses two of them. Ignorance may be a little harder.
And if you think about it, what a person likes or does not like has nothing to do with the tradition itself. It has to do with the person's own personal experiences. It's like me saying I have a problem with you, because you remind me of somebody I don't like. That's not really your fault, is it?
So, if you'd never had exposure to the Byzantine Christianity, the Mahayana emphasis upon compassion and loving-kindness would not resemble Byzantine Christianity. That similarity would not arise. In fact, it is only in the mind that a similarity occurs.
Buddha taught a lot of stuff to a lot of different types of people in 40 years, and that would probably include many yogis, sadhus and various other Hindu holy men who came to ask him questions, or to test his knowledge and wisdom. At the same time, simple farmers also came to him with their questions, their problems. My understanding is that when the Buddha spoke, so it is said, everyone understood him in their own language. I don't know if that is true, but I would not be surprised if he spoke to everyone according to their own understanding, and as we say figuratively, "spoke their language". So he very well may have discussed mantra and tantra with people, and prescribed practices for those for whom that was appropriate.
Perhaps the Buddha DID teach what is now practiced in all three Theravada, Mahayana, and Vajrayana traditions and perhaps he did not (nobody can prove what he actually said). What validates anything calling itself Buddha-Dharma is not historical proof, but testing it out in the present. This, to me, is the scientific method. By that, I mean that the results can be replicated. Consider as an analogy, Louis Pasteur. He created some of the very first vaccines. But since his time, other vaccines have also been developed, based on his discoveries. They still cure people, whether he invented them or not. Likewise, the various teachings of the different schools bring people to a perfect realization of the cessation of suffering. If somebody other than Sakyamuni had taught the Four Noble Truths, the Noble Eightfold Path, Sunyata, Co-dependent arising, and right concentration, would it still be valid? I think so.
There are some who argue that anything other than what is found in some of the Pali texts is not real Dharma. Further, that some 2,500 years of commentaries and other Buddhist writings and teachings are worthless elaborations. They argue that the Buddha was not a God, but an ordinary person like you or me, and that the Mahayana has turned Buddha into a god.
The Irony in this position is that if what the Buddha taught is valid, meaning useful, then it should be possible for people to replicate what he acheived, and for people to have continued to become enlightened even after the Buddha's passing. If that is the case, then 2,500 years of commentaries and other Buddhist writings and teachings by a variety of teachers are also valid even if they taught in their own words, and the claim that an ordinary person such as you or I can become enlightened as he did is validated.
On the other hand, if 2,500 years of commentaries and other Buddhist writings and teachings are not valid ...simply because the Historical Buddha isn't the one who gave them, or because they are not found in the Pali texts, or even because they seem to contradict some early texts, then this in fact is the view which elevates the Buddha to the status of a solitary God, because it essentially negates the claim that ordinary people, or at least people who were not Prince Siddhartha, could attain realization, because it throws all of their contributions out the window.. It also negates one of the fundamental teachings of the Buddha, that everything is constantly changing, nothing is permanent. If Buddhism were not a living, constantly evolving process, I think it would have become a stale dogma and would have dried up like the ruins of an old temple long ago.
An inward outlook develops outward insight.