I remember in a HN thread someone making the great observation that data without structure is just noise (i.e. not data at all).
You're welcome to point me at an unstructured noise source to support your point, though.
I think we may be speaking past each other.
However, it's not like the electrical noise came to be by magic -- it's the result of many interactions that have a structure, and hence impart that structure on the "noise", we just lack key facts to be able to interpret that signal.