Is it possible to do wrong-eye surgery with lasik, like reversing the prescriptions that were established pre-op?

I had all-laser Lasik a few days ago and the surgeon elected to part with tradition and do my left eye first (long story). To my concern, as he was doing it, he read out the prescriptions for the opposite eye before activating the laser. In my post-op I was assured that whatever was said, the machine can only use the specifications for each eye that are pre-programed (for example if the machine is in the left hand position, it can only use the left eye prescription). Is this true?