Yes, all USA 2012's came with the remote from the factory, but many of them were little used and evidently forgotten when the cars were sold or traded in because it seems it's about 50/50 that anyone buying a used 2012 got a remote with it, so you're not alone
The remote is the only way to preheat or precool using AC power, so without it, you're up the creek. Bad news is a new remote from Mitsu is about $1K, plus the dealer's fee to program it to work with your specific car. Good news is . . . . you can sometimes find one used for only a couple hundred and IIRC, someone here on the forum found a way to program it yourself without having to go to the stealership!
Several threads here on the forum to read up on this - I'm not going to do ALL your home work for you . . . . but all the answers ARE here!