This is orthogonal to the topic at hand. How does the chemistry of biological synapses alone result in a different type of learned model that therefore requires different types of legal treatment?

The overarching (and relevant) similarity between biological and artificial nets is the concept of connectionist distributed representations, and the projection of data onto lower dimensional manifolds. Whether the network achieves its final connectome through backpropagation or a more biologically plausible method is beside the point.

Do we know enough about how our brain functions and how neural networks functions to make this statement?

Yes, we do. Take a university level course on ML if you want the long answer.