One small correction to what @TrippyLighting said. You can, in fact, create Joint Origins on linked components. But, it's certainly not obvious that you can do so, or why you can. In fact, I had to try it just now to prove that my memory was not completely shot yet.
What is true is that you cannot make any edits to a linked component without opening that component in a separate tab. So, for instance, you cannot edit a sketch in a linked component from the top level, or even change the visibility of a body in a linked component, because those are edits to that design, and linked components are read-only in the context of the referencing design. We hope one day to change that, but it's how it is today.
And, in all local designs (where all components are defined in one design), when you place a Joint Origin, it is embedded inside of the component that owns the geometry you picked for the Joint Origin. This is, in fact, a violation of the Active Component rule. Normally, any new objects you create go into the active component. So, if you create a sketch or a work plane, it goes into the active component. Joint Origins are the one exception to that rule. Joint Origins are the only objects that can go into a non-active component. So, this combination (linked components are read-only and and Joint Origins always go into the component that owns the geometry you pick) would seem to imply exactly what my friend Peter said.
However... When we were working on linked components, we decided that this workflow was important enough to special-case. So... if you do place a Joint Origin on geometry owned by a linked component, that Joint Origin will be owned by the top-level component in your design. It's a special case to an already-special cased area.
OK, that wraps up tonight's episode of "the minutiae of Fusion functionality and history". 
After going back and investigating further, I will have to recant all of the above. I swore I was able to do this when I tested it, but whatever state I was in I am no longer able to reproduce. So, I apologize for implying that this was possible, and sending folks down the wrong path.
Jeff
Jeff Strater
Engineering Director