The Icelandic sagas were passed down orally and the one that tells about Þorgils was written a good 3-4 centuries after the events described in it. As you can imagine during such a long game of telephone, the facts get distorted over time before it is finally put in writing. It is most likely based on true events as the other Icelandic sagas are believed to be, but it is no way to know how embellished it has been to make for a more entertaining story to tell during long cold winter nights.