As a fellow driver of a 2013 X-line, I share your concern. Based on a quick trip over to RealOem.com, it appears they're telling you the truth. What's interesting is, it looks like BMW has back-dated this part to the pre-facelift version, which was never sold in the US as far as I know.
Here are the pertinent RealOEM pages:
Bumper:
http://www.realoem.com/bmw/enUS/show...diagId=51_7465
Trim:
http://www.realoem.com/bmw/enUS/show...diagId=51_7466
However, it's worth noting that your repair shop doesn't appear to have ordered the correct parts - those look like Sportline parts. You should have the chrome grill and the chrome accent stripe and the silver bottom lip, like this 2010 X-line.
http://pictures.topspeed.com/IMG/cro...-2_1600x0w.jpg Although it's not "the same", it's a better fit for the X-line package.
I assume BMW did this to cut down on the number of repair parts they have to keep in stock, now that this model is discontinued. Unfortunate, especially since a single broken piece now requires the replacement of ALL the various grille bits.