No one has yet mentioned the possibility of a slip in paternity.  You can have as many documented family trees as you like, but if there is a paternal misattribution, the family tree will be meaningless.

 

The details, including names, in the following have been changed to protect the innocent.

 

I ran across this when I was examining DNA matches for my husband Jim, at Ancestry DNA.  There was one strong match, Carl, who was Jim's strongest match besides our daughter, and who was estimated to be Jim's 2C or equivalent: 240 cM in 13 segments with longest segment 45 cM.  I looked at the family tree for Carl and could find no overlap.  In fact, I extended Carl's family tree myself, trying to find an overlap but could not find any within a reasonable timeframe.  But then my husband's known 1C2R (an older generation) also tested and he had an even stronger match with Carl.  So I now knew from which of Jim's four grandparents the match arose.  Also, I was corresponding with a cousin of Carl's (Sue) who was unrelated to Jim but who was able to tell me how strong the matches were from Carl's side (Carl wasn't interested). Eventually we realized that Carl and his cousin Sue were only half-cousins with only a half-cousin DNA match, and that Carl's nominal grandfather (shared with Sue) was probably not his actual grandfather but was likely one of my husband Jim's great-uncles. Because I knew a few descendants from that family, I was able to eliminate all but two of Jim's great-uncles from suspicion but I still haven't figured which of the remaining two was the guilty grandfather.  That will have to await DNA testing by more of the descendants of that family. 

 

So I think that when you run across unexplained relationships, you have to consider possible mistakes in paternity that don't show up in family trees.

Jocelyn Keene in Pasadena, California