I would add that the Thrulines / Common Ancestors function is based on the trees that your DNA matches have posted on Ancestry and a myriad of other Ancestry users who may or may not be related to you but have your ancestors in their trees. If they are wrong, then the Thrulines will be wrong.
Examples.
A number of trees think they have the father of one of my 3 x great grandmothers. The man is in fact her older brother, this means thrulines picks the wrong relationship between me and others who are descended from him or their common parents.
Many trees have my 2 x great grandfather married to the wrong Sarah (my 2 x great grandmother, his second wife), result being that all those descended from my 2 x g-gfather and his first wife, who should be my half third cousins or half 3C1R, don't show up a relationship at all.
I had a new match yesterday whose grandmother (according to her tree) was born in 1924 and gave birth to her father born in 1914. When I did a search on Ancestry for the actual birth year of the son, I found several more trees with the same error. Incidentally, the 1924 date is correct and the lady married in 1945 in Islington. The tree owner is my 3rd cousin twice removed, but Ancestry's algorithm obviously couldn't match a person born in 1914 with one of the same name in my tree born in 1947, so no Thruline match.
Remember, lots of people who have trees on Ancestry are only interested in making their tree as big as possible. Obviously they don't have the time to research properly thousands of people, particularly if these people are not directly related, just a distant connection to someone who married into their family generations back. But Ancestry has the perfect solution, it allows anyone to copy wholesale, great chunks of anyone else's public tree, whether it be correct or total garbage.