Wow, what a crazy day! To answer your question, your dealership didn’t rip you off. The BMW 328i does not come with a spare tire.
A few years ago, BMW stopped equipping its cars with spare tires. It enabled them to save a bit of money and claim slightly higher fuel efficiency ratings. Instead, BMW began outfitting newer cars with run-flat tires.
Run-flat tires, as the name suggests, can drive up to 150 miles following a puncture. This is meant to allow drivers to easily reach their home or an auto repair shop. Unfortunately, drivers will eventually need to replace the ruined tire.