I think my interpretation is being influenced by the fact that (a) says "Except as provided in paragraphs (b) through (h)...." I don't think the FAA would have written it like that unless they intended all of the paragraphs within that range to be exceptions. For example, look at 61.39 (a):
"Except as provided in paragraphs (b), (c), and (e) of this section, to be eligible for a practical test for a certificate or rating issued under this part, an applicant must..."
That example shows that if there is a paragraph, within a range of paragraphs, that they don't intend to be considered an exception, then they make that very clear. They don't expect the reader to infer it.
Furthermore, if (c) were NOT an exception to (a), what meaning would (c) have? What purpose would (c) serve? My understanding is that courts don't like to adopt interpretations that render parts of a law or regulation meaningless.