Here is the relationship chart they provided:
The common ancestors for this chart are Edward Thurston (1618-1707) and Elizabeth Mott (1629-1694). I looked at the line from Thurston to Pauling and my judgment is that this relationship - a 9th cousin - is Very Likely.
I wonder if Ancestry.com will provide this relationship to me in the We're Related mobile app any time soon.
What about WikiTree? They did not find a relationship for me and Linus - I think that my line is not fully populated on WikiTree. I better work on that.
What about FamilySearch Family Tree? The relationship calculator tells me that I'm related to Linus Pauling as an 8th cousin 1x removed, but from another common ancestor, Joseph Allen (1645-1704) of Dartmouth, Massachusetts. That looks correct also.