Once again I have to respond to ridiculous statements from non-orthodontists.
A doctor answered this question, stating that it was certainly possible to correct your bite without surgery or extractions! What made this assertion so unbelievable was that he made it without seeing anything else but one photo...no cephalometric x-ray, no study models, no facial photos, no evaluation of what had already been tried...nothing except his belief that his one cure fits all "functional jaw orthopedic" treatment can fix everything.
I have no idea whether you can be corrected without surgery and I certainly would not try to answer this question without a lot more information. The only thing I can say for sure is that there is no good scientific studies that show that any sort of "functional jaw orthopedics" (whatever this real means!) can produce significant skeletal changes in an adult...certainly not enough changes to compensate for a severe skeletal problem.
Want a second opinion? go see another orthodontist, or better yet two!