Since I made the original posting, I've looked into the matter and have come to agree with Martin's posting 100%. It was a story without foundation, but many of the Bearse direct and indirect descendants have come to believe it. I even submitted to mitochondrial DNA testing and came out 100% European.
A good hint that the story is false is the notion that Mary was an Indian princess. Indians did not have royalty. The Wampanoag tribe still exists at Gay Head and there is no record of Mary. It's a great story but it's without merit. That sad thing is that so many people have been misled for generations.