Can You Really Own a Position?

I've been thinking about the use of the verb to own with respect to an intellectual view.  When a student is being wishy-washy about a proposition he or she is arguing for and clearly believes, I'll tell the student to "own the position."  The command is to really make the claim and stand by it.  When you own a claim it becomes your position.  The grammatical use of the possessive there is what is fascinating.  Does that imply real ownership in some sense? 

Certainly, it is not exclusivity in the right to use.  Anyone else could own the position also in the same way.  But then anyone else could own a CD of "Kind of Blue" also, it doesn't mean you don't own your copy.  Since a view is an intellectual kind of thing, the ownership relation should have different attributes.

But is it ownership at all?  Is it a metaphorical use?  Is it a completely different sense of the word making "to own" ambiguous in the way that "bank" could mean a financial institution or the side of a river?  Or is it real ownership in the same sense?  Is it the same meaning as when we say to "own up to" some action, thereby giving it a moral connotation?  Can you really own a position?