Definitely go see a doctor. My DS had a brief stint with resisting BMs when we initiated potty training. He wasn't quite ready to begin at that time.

A week of PEG in a glass of water and a more relaxed attitude let the entire issue fade away. In Canada, the Canadian Pediatric Society has a good position statement on toilet learning:

http://www.cps.ca/documents/position/toilet-learning

Ultimately, what induced DS to use the toilet for BMs was an incentive -- something he chose that was highly motivating. I bought it and put it on a visible high shelf next to the entrance to the bathroom. DS knew it was his for the taking whenever he felt ready to use the toilet and could use it consistently for a week, and I didn't mention toileting once until he initiated the conversation a week or so later. 7 days later, the prize was his.

Note that the incentives most children choose might not be useful currency with a gifted child.

What is to give light must endure burning.