We have also used the Shriner's. My daughter has a small palm, partial thumb and 4 nubbins. I found the Shriner's to be a wealth of information and assistance. Our local Shrine Temple provided transportation (the clinic is about 6 hours away) and overnight lodging, no questions asked. Throughout the years we have been invited to all their events: Christmas, circus, picnics etc...
The closest thing they have to a catch is that it is for children. Depending on the facility, you may age out at 18 and somebody told me one place was 22 if the patient was still in school. Once your child is grown and out on their own, they will no longer be eligible for treatment at their facility.
My grandfather was a Shriner; these are guys who really, really want to help children. Of course they like to ride on the little cars, motorcycles etc... to help raise awareness and raise money to help children. They found a niche to fill and they do it extraordinarily well.
I believe (but I could be wrong) that the doctors they select donate their time as well. Sometimes it is difficult to schedule or a long wait to get an appointment to see the doctor because he/she is only at the clinic one day a month or so. (This may vary and they may have changed it since we were last there). The PT, OT and other staff are there much more frequently. Their facilities are phenomenal and the personal service they offer is top notch.
We have never been for a surgery, but have been for consultations and to work with the PT as we develop a device for playing the violin and gymnastics for my daughter. I would highly recommend the Shriner's to all, without fear and without hesitation.