The Orton-Gillingham method is focused on multi-sensory learning combined with consistent review and individualized instruction. Because of this, it is an incredibly flexible method that allows the student to go at their own pace. It works because it doesn't create any gaps in student learning, making it very effective. I mean if it's still around 90 years later... must mean something works! Granted this method may not work for every student, but it does wonders for others.
I encourage you to listen to the requests of the parent and pay attention to the needs of the child. At the end of the day, they know their child better than you do. Also, each student learns differently (whether they are in special ed or general ed), so if orton-gillingham works for that student, then it's a great thing! :)