Religions rarely appear because someone lied. More often they are results of honest try to understand the world connected with some kind of mystic revelation. The mystic revelation might be connected to dreams, hallucinations, delusions of grandeur, but they might be as well realizations of some profound truths which occur to the "prophet" in such a groundbreaking way that he or she decides that it had to come from something supernatural.
In the theravadin tradition, Buddha Gautama decided to sit in meditation under a tree until he reaches Enlightenment. When he did it was to him as if his eyes opened again and now he saw the whole world in a different way. Before that moment he was a vedic ascetic (it would be anachronistic to say that he was a Hindu). After, his understanding of the world changed so much that he built his whole system from anew and was even afraid that people would not be able to understand it. If he was right or wrong is a different question, but it seems that he was honest when he taught it. If people had perfect memory it would not prevent the spread of Buddhism. In fact, it is claimed that one of the disciples of Gautama had perfect memory and he was crucial in preserving his teachings after Gautama passed away.
Mani was the founder of now extinct religion called Manichaeism (surprise, surprise). He lived in the III century in the second Persian Empire (nowadays Iraq and Iran) and spoke Syriac. He connected beliefs from a wide range of gnostic sects which made something of a continuum between Christianity and Zoroastrianism, added a bit of early Buddhism to it and wrote a book full of cosmic beings and complex theology. He claimed to be inspired by his "heavenly twin", a being which appeared to him. It sounds much more like a lie than what Buddha did, but liars usually has a purpose in their lying. I didn't look like Mani had a purpose. He made a bold move and presented the book to his king, Shapur I, who was not impressed but nevertheless allowed Mani to preach his religion. But the king's son, Bahram, was not so tolerant and Mani died in his prison in a very gore way some years later. I would say Mani was guy who made something up but then started to believe it himself. If by "perfect memory" you mean that he would not fall into delusion then there would probably was no Manichaeism (which is extinct anyway and its greatest legacy is how it influenced Red Turbans rebellion in medieval China, as well as some small gnostic sects in Middle East). But maybe Mani would have been remembered as the first author of epic fantasy ;)
On the other hand there are guys like Bahá'u'lláh, the founder of Bahai Faith or Guru Nanak, who founded Sikhism. We can't know for sure how true are stories about their revelations and how much they just made up, but it seems that they both worked for common good, and not just their own profit. Especially Bahá'u'lláh was a very peaceful person, a poet, who believed that we can all accept our differences and live in peace (after all, all prophets preached the same religion, didn't they? ;) ). In effect, he spent a large part of his life in prison, because Islamic authorities didn't really agree with him.
Guru Nanak was (I think) more successful. He lived in the XV-XVI century in what is now Pakistan and he claimed to have a revelation from God which connected Islam and Hinduism. Pretty convenient for someone living in the territory where these both cultures mixed and clashed all the time, no? ;) I always wonder why God didn't reveal herself to some indigenous peoples in, let's say, Borneo and gave them the same message as to Arabs, for example. That would solve a lot of problems about which religion is true.
But anyway, even if Nanak made that up, his teachings were an attempt to improve relations between Muslims and Hindus. For sure he didn't make up stories about the past, so perfect memory wouldn't change anything.
I know I'm not answering your question directly - my point is, in my opinion perfect memory would not change much in people's beliefs, because beliefs are rarely based on lies which could be exposed.