Usually, when people turn their horses to the inside before a lope, its a cue to let them know the direction. Some horses tend to associate a particular lead with the direction it is most commonly used in.
It can happen with horses who are lunged often, or just horses that aren't really asked to do a lot of loping exercises. Certainly, it's not a bad thing.
Someone posted earlier that turning their head to the outside helps them to fall into their lead better. That's the way I see it. If you expose the inside leg by turning their front end to the outside, it allows you to push the lead forward with your outside leg. It makes better sense when you are used to doing it.
It can also keep their hind end from becoming too lazy by forcing the inside hind leg further inside, and away from the outside hind leg. It's discouraged by some judges, but by moving their hind end a bit off the rail, you can help to improve movement.
I don't think your trainer is crazy. There are so many ways to train a horse, it's not always about what's right or wrong in the grand scheme, but what works best for you and your horse.