In a cricket tournament organised by the ICC, a total of $15$ teams participated. Australia, as usual won the tournament by scoring the maximum number of points. The tournament is organised as a single round robin tournament - where each team plays with every other team exactly once. $3$ points are awarded for a win, $2$ points are awarded for a tie/washed out match and $1$ point is awarded for a loss. Zimbabwe had the lowest score (in terms of points) at the end of the tournament. Zimbabwe scored a total of $21$ points. All the $15$ national teams got a distinct score (in terms of points scored). It is also known that at least one match played by the Australian team was tied/washed out. Which of the following is always true for the Australian team?