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....and the trainer said that maybe that wasn't exactly right because a "real runner" strives to make a 14 minute mile on the ground
A 14 minute mile is SLOOOOOOOOOW, for a runner. That isn't even a running pace. I think you probably did do a mile in 10 minutes. That is a nice steady pace (not fast, but not super slow) for a jogger. I am a "real runner" and I do about a 9 to 10-minute-mile for most miles. Not slow, but not racing by any means either. I think the machine could easily have been accurate. By what you've said, the machine sounds more accurate than the trainer.