Correct, the valve is probably stuck closed with the problem you are getting. You are not getting a low flow code because the exhaust isn't changing one bit when it "opens" the valve. No flow is not considered low flow in these situations.
I am not versed in the exact unit that the crossfire uses as a valve, but often on pretty much every other system out there they just get stuck with carbon and by removing them, scraping the crap off and giving them a slight whack on the valve frees them up and can get them working again without replacement. Since you already have a new one I would slap it on. Check to make sure the passages aren't blocked off with carbon, which is also a common problem in EGR circuits.