For whatever reason, my Ally toons can't see the 'Taming Kalimdor' dailies, and my Horde toons can't see the 'Taming Eastern Kingdoms' dailies. So for your example, Durin Darkhammer, only my Ally toons are able to get a daily. I suspect that this is due somehow to the fact that I did everything on an Ally toon first, and that EK is tied to Ally and Kalimdor to Horde, but I can't prove it. But trying an Ally toon might let you get a daily from him.
Unless you're already Ally, then I have no idea. And all of my toons can get dailies from the Outlands tamers at this point, so if you can't then I don't know the issue.