My orthodontist claims that my overbite could never be corrected due to the thickness of my teeth? Is this true? (Photo)

Have you considered seeing a surgeon. Your jaw might be too small to handle just orthodontic treatment. 

If your teeth are large and you are bothered by large width as well which creates a significant overjet and overbite space with the lower teeth, one option would be for your dentist to perform a minor amount of interproximal reduction or IPR.This procedure would recontour/file a small amount of tooth enamel (often less than .5mm), most commonly, between the upper anterior teeth, to create the space and allow movement necessary to correct most overjet/overbite concerns. IPR is commonly done with Invisalign clear aligned therapy to facilitate movement of teeth. You should always consider a second opinion for any issue you encounter before during or after treatment.