Other than a few wild claims outside of science, fitness has never been proposed as a cause of evolution. It is an outcome of the variation of genotypes in a population in response to the environment. I've only seen one person make this claim here and the level of understanding of science from that source is dubious at best.
Fitness is a measure of the reproductive success of individuals and populations that quantifies the response of a genotype to the selection of the environment in the number of successful reproductions. Some genotypes have a greater propensity to be reproduced than others do in a given environment.
If a mutation leads to a phenotype of increased susceptibility to a disease, then the presence of that disease in the population would limit the reproductive success of any member of the population with that increased susceptibility. Down to zero in some cases. Unfortunately, organisms, including humans, are not equally fit. Or perhaps for the population, fortunately, since equal susceptibility to a mortality factor could very likely mean extinction.
Regarding the environment, it is all the abiotic and biotic components experienced by an individual and a population. And includes the internal as well as the external. It is not merely the weather or the climate, but does include those.
Accidents do happen and chance events can remove the more fit, fit and least fit without regard to fitness. In the words of John Maynard Smith, "If the first human infant with a gene for levitation were struck by lightning in its pram, this would not prove the new genotype to have low fitness, but only that the particular child was unlucky."
A defect in a gene that results in a three-legged rabbit would likely render that rabbit less fit and for an obvious reason. A rabbit with this genotype and phenotype would more than likely suffer a fitness deficit in a number of environments where rabbits are otherwise successfully able to exist.