Nobody claimed that, that I'm aware of. As I understand it, the various approaches are all descriptive; the ultimate reality is unknowable, so we must find appropriate and useful descriptions of how things behave.
When people argue that DNA is algorithmic, they are arguing that an algorithmic description is a viable description of how it behaves - it has explanatory and predictive power.
When people say the brain is computational and algorithmic, they are saying that this is a viable description of how it behaves. They say this partly because it has been shown that the function of parts of the system - isolated neural networks - can be precisely described and modeled using computation and algorithms. Since it appears that the whole system is composed of an assembly of these networks, it seems reasonable to suppose that the whole system can be described in these terms. There are other influencing factors beyond the connectivity of the elements, but these influences on the system can also be treated computationally.
There may well be other ways of describing the system and other ways of modeling it; I'm not familiar with the alternatives, but the algorithmic, computational approach has a lot of explanatory power, and continues to produce useful explanations, results, and predictions.