When I think about it, it's more likely to me that it leads to systematic errors and the appearance of precision than actually uncovering anything.

When I look at the Bulls, it's just a confusing mess.

Looking at the players' play by position and 5 man units you can make some extrapolations, and they don't confirm what I see with my eyes.
Hinrich has played 48% of the PG minutes and 12% of the SG minutes. Gordon's played 44% of the SG minutes and 12% of the PG minutes.  Based on the 5 man units, one see that:

1. Hinrich's "SG" minutes must mostly come with Duhon at the point.
   
2. Gordon's "PG" minutes must mostly come with Hughes at SG.
   
3. When Hinrich and Gordon play together, Kirk is listed as the PG and Gordon the SG.  But in reality, Kirk often defends the opposing SGs and Gordon defends the opposing PG.

I take 2 to mean that Ben's dPER as a PG is probably accurate because it mostly reflects his minutes with Hughes and Ben can be expected to be guarding PGs when he's paired with Hughes.  So Ben's dPER against PGs is probably fairly accurate.  It's 20.3, which is similarly abysmal to Kirk's.

I take 3 to mean that, with some level of uncertainty, we can imagine that much of Kirk's "dPER as a PG" is actually Gordon's "dPER as a PG" because when Kirk and Ben are in there together, Ben is more often guarding the PGs.  Likewise, Kirk should really be "responsible" for Ben's "dPER as a SG" because he's probably defending the SGs in that situation.

So you switch their dPERs, and you see that Ben's dPER when playing with Kirk should really be 16.9 and Kirk's should really be 19.3.

That sort of makes sense and sort of doesn't.  Kirk's 19.3 dPER when we believe he's defending SGs with Ben is similar to his 20 dPER when we know he's defending SGs with Chris Duhon on the floor.  So we have some consistency to say that Hinrich is bad defender against SGs no matter how you cut it.

On the other hand, you get a pretty big change in Gordon's numbers.  Gordon with Hughes has a dPER of 20.3. Gordon with Hinrich has a dPER of 16.9 against PGs.  That's still not great, but it's a pretty substantial improvement, and I don't see any obvious way to account for it.

Well, except to say that method credits him with some of Hinrich's defense on PGs, and to say that maybe Gordon actually does defend SGs more often.  In short, all of this thinking about it just leads one back to the starting point.  Without actually knowing the defensive assignments, there's just no way to divide things up.

I think the problem is even worse than that, though, because often teams take unusual steps to defend good players in key situations (like San Antonio using Bruce Bown on both Steve Nash and Dirk Nowitski, and how in key stretches when we played them, they'd sic him on Gordon).  Those are the situations, I'd think, when defense really matters the most, and in those cases positional analysis gets completely thrown out the window.