Just ask if the machine can cut side-winder keys. It's no difference to, say, a Honda key. The really high-end machine can cut key without the original, provided that you know the ISO code for the key, which is mapped to your VIN. Unfortunately this mapping is held in BMW headquarter
Another note about programming. There's no reason why a "cheap key" cannot be programmed unless it's been programmed before. The Elmos chip allows only one-time programming and it's only a $2 piece of silicon
Nevertheless, I agree that for a total peace of mind, cough $660 to get it from BMW. To get it cut somewhere else, you're giving away the secret that will enable a third party to cut more key to steal your car if they want to.