Royal Connections?

I recently found a family tree that, if you follow enough of the branches back, connects our family to Scottish Royalty.

Of course, without seeing any original records (what genealogists call Primary Sources), all of these links must be viewed with a bit of skepticism. But, if you want to see the tree, go to the The Large Version Of The Chew Family Tree website, then follow these links:

(You will start on the page that lists Benjamin B Truax, a Great-Great-Great Grandfather of Chester Carson)

Click on his wife, Rebecca Abagail Stillwell, then
Click on her father, Elias Stillwell Sr., then
Click on his mother, Abigail Hopton, then
Click on her father, Robert Hopton Sr., then
Click on his father, Arthur Hopton, then
Click on his father, Owen Hopton... keep going, click on:
his father George, then his father William, then his father John, then his mother Margaret Pert. You're getting close now.
Click on her mother, Joane le Scrope, then her father Sir Stephen le Scrope.
Click on his mother Juetta de Ros, then her father Sir William de Ros II.
You're back to about 1244 at this point.
Next click on his mother Isabella Avenal of Scotland, and then
William "The Lion" King of Scots

From here you can sort of browse around. There are a number of noblemen, kings, sirs, etc.

Are we really related? Maybe. A DNA test might be the only conclusive test, since so many records over the years have been either destroyed, misplaced, or misrecorded.