Very good points! I would add that we don't yet have a complete model of the computational properties of even a non-neural cell, even though we know that all cells exhibit simplistic perception and decision-making.

This is not to say that we should expect some non-turing weirdness or anything 'mystical' like that, but that we just haven't taken the time to analyze the exact mechanisms and to model cells at this level well enough to be able to say that they are similar to any particular computational structure. Thus, to claim that the brain in its entirety is similar to any particular computational structure such as an NN is either wrong or trivial - the only level at which 'similarity' can be claimed is that they are both useful in computation, and likely turing complete. Anything more specific is fanciful thinking.