People do what they *want* to do
It is a given that the only actions a person does that are relevant to the idea of selflessness are those that the person chooses to do. If a person chooses to do something, then he *wants* to do it. Therefore, he is fulfilling his own interest and satisfying his own desire. In conclusion, any person's actions will fulfill their own goals, regardless of any other person's interests. What is in question is whether there exists a person who chooses to help another person in order to help that person. This would be analogous to "I eat food to eat food" or "I recycle in order to recycle" or "I help people for no reason"
The easy question is: Does there exist a person who acts, in any manner, only to fulfill a desire to act in that manner? Obviously not. Every desire for action must be wedded to a desire for the consequences of that action, unless the action is unconscious/impulsive and irrelevant to the discussion.