There is another answer to the question of the Ran. Several acharonim say that the Rambam who opines that a safek is permitted m’d’oraisa applies only to a safek issur. A safek if one has fulfilled a mitzvah is not to be ruled leniently. This is because the Torah wants us to perform mitzvos and until we are certain that we have performed the mitzvah we must ensure that we fulfill it properly.
Perhaps we can apply this concept to a mitzvah m’d’rabanan and say that although a safek issur d’rabanan is to be ruled leniently, a mitzvah m’d’rabanan must be dealt with stringently to ensure that we fulfill it properly.