TThere’s a critical difference between subject based knowledge organization schemes created to organize books and other documents, (e.g. LCC, DDC, and LCSH), which are defined in terms of the things which a work is about, and rigorous, class based ontologies that are based on the properties of the things themselves.
Some relationships may be valid in terms of subjects, but may not apply directly to the things themselves. For example, a car wheels are part of cars, and cars are a type of vehicle. These relationships are always* true, and are examples of two different types of hierarchical relationships – partitive (is-part-of) (BTP) , and generic (is-a-kind-of) (BTG)
Always-aboutness is the combination of all the different types of hierarchical relationship – this is the Broader Term (BT) relationship. In terms of aboutness, we can easily say that everything about car wheels is always about cars, and everything about cars is always about vehicles. We can also directly infer that everything about car wheels must always be about vehicles. In other words, the always-aboutness relationship must be transitive.
Transitivity doesn’t hold when you mix different types of hierarchy – car wheels are not a kind of vehicle, but that has nothing to do with the transitivity of plain unqualified Broader Term.
When thinking about systems for organizing information, it’s absolutely critical to remember the difference between the document, and the thing the document is about.
Or in other words:

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I have a question. Is a unicorn a doorbell?
Very thought provoking indeed – thank you. There seem to be two insights here, and I wonder if they’ve got a bit tangled. Sorry about the way I labour what follows. I wish I had the magic touch.
On the one hand, you emphasise that subject headings are to do with the way in which documents are about things. Given a set of documents, one might imagining classifying each document by fixing for it the appropriate set of subject headings, each subject heading naming a thing the document was ‘about’. This involves looking at the document. One might in theory imagine this being done without any hierarchy being defined between subjects, so that the classifier was required to ask whether a particular book was about car wheels and whether it was about cars and whether it was about vehicles, and so on. Lots of judgement and looking at documents involved here! Once aboutness had been determined for each (document, subject heading), one might then imagine inducing a subject heading Broader Term relation in which
sBt iff for all d (d about t implies d about s).
This is clearly transitive. Note that on this document-centred view adding a new document to the collection could invalidate a previously valid Broader Term relation. To adapt our example, suppose that every book in the collection judged to be about car tyres had been judged to be about cars and had also been judged to be about vehicles. However a new acquisition How to grow flowers in car tyres was judged by the classifer to be about car tyres but not about vehicles. We would then need to discard vehicles as a Broader Term of car tyres (and also discard – depending whether we judge the acquisition to be about cars – either cars as a Broader Term of car tyres, or vehicles as a Broader Term of cars)
On the other hand, as you say, once one has a class-based ontology one can define a concept-based Broader Term relation as the ‘combination of all the different types of hierarchical relationship’ within that ontology, i.e. taking
sCt iff (t is-part-of s, or t is-a-kind-of s, or etc.)
this alternative Broader Term relation can be defined as
D=the transitive closure of C.
In this labour there’s no looking at documents, only thinking hard about concepts.
Now, you say, plausibly, there’s some connection between B and D. What is it?
D will be rather weak, i.e. it will hold fairly often and surely more often than B. That is, it seems implausible to me that sDt implies sBt.
But maybe your line of thought is that any subject heading broader than relation B induced from aboutness must be somehow explicable in terms of conceptual relations.
That is, the connection goes the other way round: sBt implies sDt. Which seems plausible.
Am I confused?
So if I was looking for something about someone or a concept that crossed the boundaries between two or more subjects then I should look for the chassis of the matter rather than the influences that carried it to where it was finally going to end up?
For example Jean Arp, ultimately an abstract artist renowned for sculptors using various media, but previous a founder member of the Dada movement, and also by association, as he worked with Max Ernst, could also be looked for under Bauhaus Modernism pre-Nazi Germany.
In this case the wheels are in the shape of Modern Dadas, but the chassis of the matter is abstract?