Harper Hospital makes a cameo on "The Good Wife"

I'm catching up with last night's episode of "The Good Wife" on my TiVo tonight. Story begins inside a hospital, presumably in Chicago where the show is set. Cut to an outside shot of the hospital and it's our very own Harper Hospital in the DMC. They cropped it tightly so no identifying signs were visible. It was on the screen for maybe 3 seconds. [[Thanks to my trusty TiVo I was able to go back and watch it again to make sure my eyes weren't paying tricks on me.)

As far as I can tell, that's the only part of the episode that was shot in Detroit. Is this a spin-off of the film tax credit? Do the producers save a few bucks by filming that little bit here? Or did they just run out of hospitals in Chicago that haven't already had a starring role in a tv show?

Yes, they changed the name to "HARBOR HOSPITAL"