You are quite correct in saying that Shakespeare would not get top marks for his knowledge of Scottish history. However, the most important word in your post is "apparently". This suggests that you have got back so far yourself, carefully checking all the documentation, then have linked to someone else's research. I would advise you to check out all the documentation which links you to this older "research" first. If it stands up, then you'll have to do the same for every step back in time. The risk is that you spend ages researching people that turn out not to be ancestors.
What is the furthest back ancestor you have definite, personally checked evidence for?
