Survival of the fittest? Is it true that only the fittest will survive?

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According to the theory of evolution, all animal life on earth has evolved from a common ancestor. This process has supposedly occured over an immense time and followed a step-by-step sequence from primitive to advanced forms of life. This would mean plant life first appeared and developed, followed much later by the animal life. This idea is contradicted by the fossil record, which shows complex plant and animal life first appearing together in the geologic column during the Cambrian era. Another obstacle to this theory is the interdependent relationships between living things, called symbiosis, in which completely different forms of life depend on each other to exist. Darwin's theory of biological change was based on competition, or survival of the fittest, among the individuals making up a species. He admitted: "If it could be proved that any part of the structure of any one species had been formed for the exclusive good of another species, it would annihilate my theory, for such could not have been produced through natural selection"(Darwin, p. 164). http://www.ucg.org/booklets/EV/competitionsymbiosis.htm If we "survival of the fittest" is the case, why is that another species depends on the other to live? Why do they help each other? Example is the Egyptian plover and a Nile croc, how could such diverse animals, which normally have a predator-victim relationship, become partners in clean-up operation?