I know, that the grey slash buttons would be the ones to uncheck. They're not there, when I try to derive the Assembly.
Compare the following screenshot (when trying to derive the part without the detour through the assembly) with the one above:

The two solids within the part are not proposed for unchecking them or not, when deriving the assembly. There I can only choose the entire Part with all its bodies, or nothing (plus the two bodies of the part beeing merged unsolicitedly).
Toggling the export-flag for one of the bodies has no effect - and would be rather counterproductive in my scenario, because I want to export the other body to another derived part.
My convoluted deriving might seem a little bit far fetched, but I came up with that, because I am trying to design a super-complex 3d-Print-Part-Couple, which has become almost unmaintainable when trying to draw it as a single part file with over 300 design features. So I split it up into managable portions, which I then want to merge into two single parts for printing
Anyway, I can though prevent one of the bodies beeing imported by controlling its visibility, and then use the design view associativity-approach. Plus, I CAN derive the now invisible body to another, simple derived part (i.e. without taking a detour through an assembly). So, I'll go with that, as this way I can achieve what I want, but still I'd say Inventor's behaviour is not very consistent here.
So next question: How do I prevent someone else fumbling with my visibilities, and mess up my derived part? I see, that I can lock the design view... and again I am thinking: WTF??
I lock it, but can still toggle the visibilities of its components (without effecting my derived part 😮 ) ... and am prompted to save the assembly upon closing it (due to the "view-rep (dirty)"*-flag beeing raised) ... just to see, that my changes, which I have made although I was not supposed to be able to make any changes, have been discarded when I reopen the file after granting the save prompt (which it does not, when the file has'nt really been closed, because it's still open in the context of a referencing assembly -> in this case I'll have to switch to and fro between two design views to flush my illegal visibility changes).
Is this supposed to be intended behaviour? Doesn't make sense to me!
*BTW: What's the difference between "view rep (dirty)" and "view rep (smudged)"