I'd call that a defect for sure. Send it back, or heat it up and bend it into place, followed by prompt cooling.
I don't have the Spigen Case, but I had the issue with my iPhone's Commuter case. I ended up getting this
cable:
http://ecx.images-amazon.com/images/I/31aUuIbkRtL._SY300_.jpg
And then this one to replace it when it got bent up too much.
http://ecx.images-amazon.com/images/I/31tt6a2NbqL._SX300_.jpg
I DEFINITELY prefer the white one, as it has seemed tougher, and the grip on the plug is more comfortable to use. It also has a better rating on
Amazon's reviews. But I can confirm they fit the Cmmmuter's "narrow" aux port, and I never had another cable that worked with the case because of said port's diameter. I'd assume you'd be safe with this one. Order it for sure, Best Buy's in-store price is pretty steep on the black one, and I don't know if they carry the white at all.