Is my friend's friend also my friend?

Well, are they really? Just let me tell you a story. Paul following on a suggestion from his good friend Bill decides to fly over to Park City to sample the incredible snow we've received early April. Paul, who is well-to-do, but a cheapskate, will stay at Paul's, but Paul feels obligated to get his very best friend someone good to ski with; you see, Paul is pretty old, but still a relatively good skier. So Bill sends an email to Mike, a neighbor who happens to be a very, very good skier and asks him to ski with Paul. Mike has skied once with Paul, barely knows him and is by no means his “friend.”

Like anyone else, Mike has a schedule, so he warns Bill that he can't commit for sure to ski with his neighbor's friend, but will do his best. Bill emails Mike back that his friend Paul would be utterly disappointed if he couldn't ski with him. Pushed to the brink, Mike finally devotes a day to Paul who has a blast, and towards the end of the day, barely offers him a “cup of tea or coffee” for his time, which he declines. Mike is of the opinion that, next time, Paul should hire a ski instructor for the day. Since when do your neighbor's friends automatically become your friends?