Question: I have deep faith in Buddhism as a logical and systematic approach, almost philosophical, to life. But the other bits of it, the rebirth bits (where do we find proof? I know many people are said to be able to remember their past lives but perhaps they're just over imaginative? coincidental recounting of incidents that are taken as one's past life, or even schizophrenic people?), as well as the parts of being reborn in the Pure Land if one were to harbour pure thoughts while reciting Namo Amitabha - but how can it be fair to the poor man who spends his entire life reciting it well but nearing his death, loses concentration for a split second because of something beyond his control, e.g loud noise outside his hospital ward which is something beyond his control, thus, losing a wonderful chance to be reborn in the Pure Land, as opposed to someone who has never chanted Namo Amitabha and suddenly, converts to a Pure Land follower and goes to the Pure Land just before he dies? It's so unfair.
Response: First, those who can truly remember their past lives are extremely rare and have much good fortune. Others may be "over imaginative" as you said or perhaps unable to really tell what the "memories" are.
Second, those who are reborn in the Pure Land exhibit certain signs such as saying in advance when they will pass from this life, passing away without any sign of illness, passing away at will, remaining standing or sitting after passing. Or the body may remain flexible and maintain a good color many hours after death. The signs indicating rebirth are to be carefully checked and validated before being made public.
As for the conditions surrounding our death, we need to conserve our good fortune to create the right condition as we are dying. No other time is as important as this as our last moments lead us to our future rebirths. The person who suddenly encounters bad conditions, like that loud noise, did not have enough good fortune to ensure a peaceful, quiet environment.
And that person who hears of the Pure Land at the last moments and dies while chanting is unbelievably rare! We cannot count on that happening to us. This exceptional occurrence happens because the person was a practitioner in past lifetimes and conserved his good fortune in this lifetime. So he had the wonderful conditions to be conscious, to encounter a good spiritual advisor, to immediately and completely believe in the Pure Land, and to be able to practice, all while facing death. The coming together of all these conditions is unbelievably rare and the direct result of profound previous practice.