Any claim that scientists have not been presenting the full empirical evidence about evolution is blatantly false. Whenever there has been any plausible evidence that suggests problems with the received view of evolution, scientists have been excited to investigate them (Sarkar 2007, Chapter 10). In the 1960s scientists were excited about the proposal that most evolutionary changes at the molecular level were "neutral" and not selected for. In the 1980s scientists debated the possibility that evolution consists of small bursts of change followed by long periods of stasis (what Stephen Jay Gould and Niles Eldredge called "punctuated equilibrium"). In the 1990s biologists debated whether bacterial mutations were "directional," that is, more likely to occur in conditions favorable to them than in those that were not.
The overall view of evolution has so far barely been modified to respond to all these challenges and eighty years of new data. Our confidence in the correctness of the models that comprise the theory of evolution is exactly because of the "specifics" of the evidence.
Additionally, there is a strong disanalogy between scientific reasoning and legal reasoning in the Anglo-American context. Though there are plenty of scientific disputes, the scientific method is not in principle adversarial with each side arguing its case to the detriment of the other. Rather, scientific research is investigative and all honest workers have to consider all the evidence. This is exactly what creationists do not practice even when they claim to be concerned with the "specifics."