I think you're confounding/conflating/confusing the inline (html) TOC and the NCX navigation TOC. Kindlegen (Previewer) doesn't create an inline TOC, so you must be referring to the navigational (ncx) TOC when you say Kindlegen's version is "OK."
I suspect the the NCX TOC on the calibre converted AZW3 is OK too. Which means that the automatically created/detected inline (html) toc that calibre builds is where you're having trouble.
Unfortunately, it must be the Structure Detection settings you're using in calibre that are at fault, because using calibre's default settings... I get the same (expected and correct) NCX and inline TOC using calibre or Kindlegen. I definitely don't see any of the footnotes in either TOC.
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