Surprising noun order involving the の particle

Question

I am puzzled by the word ordering in the following sentence:

そのうちの一つの[箱]{はこ}は私のです。

This sounds unnatural to me, though I was told that this is correct by a native speaker (who was not able to explain why). Whenever I've encountered this linking/nominalization/possessive particle before, the nouns were ordered with increasing specificity. (e.g. 友達の本の名前).

Based on that principle, I would have expected the sentence to read

その[箱]{はこ}のうちの一つは私のです。

I.e.:

1. most general: 箱 (box(es)),
2. more specific 箱のうち (amongst the boxes)
3. most specific: 箱のうちの一つ (one of the boxes)

What am I missing?

Answer 1

If I'm not mistaken, I think there are two acceptable ways to say this in English, too:

そのうちの一つの箱は私のです。
One box among those is mine. (more literally) Among those, one box is mine.

その箱のうちの一つは私のです。
One of those boxes is mine.

It's true the former looks slightly less-organized, but the nuance is fairly small in spoken language.

Answer 2

Personally, my interpretation of "そのうち" in this case would be "among those things". Hence, it's referring to a collection of non-descript items that also happens to include a box among them.