I don't see it that way. Usually a game player sticks out like a sore thumb. Unless of course we are talking about some deeper mask philosophical Cow thread part 3 way. In which case I would play.
Why is that assessment the most consistent with your game? What game would need to make an act of honest friendship into an act of rejection? You omitted important parts of that story that made it seem like it was the opposite of what it really was. Why? If my BFF decided to quit drinking there is no way in hell I would act as her mentor. Did she get on your nerves and you just needed a way to distance yourself or did you really like her?