Red Hand of Ulster

I was reading my assignment for my surveying class yesterday at a computer in the library. The girl sitting across from me was working on something about heraldry with a guy from her class. It was pretty quiet where I was sitting, so I could overhear their whole conversation. Anyway, she pulled up her family crest, which was the O'Neill family crest. It looked something like this:

The guy sitting next to her why her crest had a red hand in it, and she told this story (I'll be paraphrasing here):

There were two brothers racing toward Ireland. They might have been princes from England. I'm not sure. All I know is that they were from the O'Neill clan. Anyway, they heard about how beautiful Northern Ireland (Ulster) was and the wanted to take it over. They decided to have a race and the first person to touch land would become the ruler of Ulster and the other one would have to return home. The race was pretty close. When the brothers were close to the shore, the one who was losing saw that the other would win. In desperation, he cut off his hand and threw it to shore! By doing so, he was the first one to "touch land" and became the ruler of Ulster. The hand in the crest is red because the hand was probably really bloody.

The guy asked the girl if that story is true, and she kind of laughed and said, "probably not." I'm guessing that at least PART of the story has to be true. Most legends are based on some sort of fact. If anyone knows anything else about this legend, let me know. All I know is what I overheard.