It is true that a lot of members of our, and most other species, suffer from cancer, but it is still not ubiquitous nor does it exist throughout the individual's life.
If a species existed, in which all, or almost all of its members suffered from the same pathology, and that pathology showed up and existed throughout the organism's life, and this pathology has always existed within the species, would that violate natural selection enough to consider the current body of theory of evolution falsified?
To be clear, it is recognized that natural selection is not the only process which occurs during evolution, but it is pretty safe to say that enough of our body of theory on evolution rests with the validity of natural selection that if natural selection were falsified, so would the body as a whole, and we would need to rework our theories.
Consider what is said in Evolutionary dynamics in structured populations.
An evolving population consists of reproducing individuals, which are information carriers. When they reproduce, they pass on information. New mutants arise if this process involves mistakes. Natural selection emerges if mutants reproduce at different rates and compete for limiting resources.
In other words, evolutionary dynamics implies natural selection. A violation of natural selection therefore would make the current theory on evolutionary dynamics less likely. Now, it could be that other processes are so powerful that they completely override natural selection, but to find a species in which natural selection has totally failed to weed out a near universal illness should present a problem for current evolutionary theory.