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Now help me out here... Are you saying that a message from Manager to Car establishes a relationship between them without that relationship being an association?
To paraphrase Dr McCoy from from Star Trek, "Yes Jim, it's an Association, but not as we know it!"

UML states explicitly that a named navigable association end IS an attribute. Therefore, a (binary) Association is about static structure. Thus, in your initial example, Car has an explicit attribute member, MyWheel which establishes the Association shown in the diagram, for the reasons above.
So what ARE the relationships when Manager uses other classes to do it's job? Well, what is an Injector? "I direct a second party to be aware of (associated with) a third party..." How does that sound?
If you like that, then you have a ternary - not binary relationship between three Classifiers. I'd model it as such...
I'd stereotype the Association "lozenge" as "setter injection", stereotype the AssociationEnd between the lozenge and Manager as "injector", the AssociationEnd between the lozenge and Wheel as "injection" and the AssociationEnd between the lozenge and Car as "injectee".
You can thus read the Association narratively as: "Manager is the injector that injects Wheel into Car".
From a "compilable model" point of view, it would be a constraint that when you create a ternary Association with such stereotyping, there must also exist a binary Association (attributive) from the injectee to injection.
I have a similar problem when I'm creating code artifacts for source components using my interface: I have to follow a ternary Association from the component to the Artifact and Class ("For this Component I require the following Class to be in that Artifact.")
BTW: Yesterday (now) I emitted my first operation body, having got around a problem with CodeDOM not understanding the difference between a string and an symbolic literal.. :-)
HTH,
Paolo
BTW, in the absence of the ternary Association, you can do it with a LOT of cross-dependencies... That's why I made the first statement in the original post...