They base this on the statement in the Mishna, כל המזכה את הרבים אין חטא בא על ידו( A sin does not come to anyone that brings merit to many people). That is supposed to counter [oppose] the effect of כל המחטיא את הרבים אין מספיקים בידו לעשות תשובה ( One who has caused sin to many people is prevented from repentance.)
But you can see the effects are not opposed. Let's say that, for example, one has been מחטיא את הרבים (caused many to sin) up until today, and now he wants to start being מזכה את הרבים (bringing merit to many). Then he would be prevented from future sin, but still be unable to repent on past sin.
But what the books of Musar are suggesting is still valid. The effects of bringing many to sin and bring merit to many are still opposed in their effects. So it is still a good idea to stop bringing people to sin, and to begin to bring merit to people.
One still might not be able to repent, but still even a little bit of good is also good.
[The idea of bringing merit to many is brought in the books of the disciples of Reb Israel Salanter and that is no surprise. But you also find it in the classical mediaeval books of Musar.]
You can learn what ever books of Musar you like, but my own tastes have changed during the years. If I could I would try to get all the books of the son and grandsons of the Rambam, Reb Avraham and later descendants of the Rambam. [They were printed recently in Israel].
I saw one time in Uman someone had a copy of volume that had a lot of the books of the descendants of the Rambam in it. Interesting also to note another fellow had the entire Mishne Torah in one volume (no commentary)!! That I thought was really neat. I think it was based on the Yemenite manuscript. [That makes it easy to do the program of the Rambam of learning the Mishne Torah and then the Physics of Aristotle and then the Metaphysics of Aristotle.]
What I suggest is to have one session in the Mishne Torah of the Rambam straight and another in the Avi Ezri of Rav Shach (Elazar Menachem Shach from Ponovitch) straight through from beginning to end.
[This is just for a first reading of the Mishne Torah. The second time around I recommend doing with with the Keseph Mishna. I mean this for the 45 minute halacha session in the morning. This should not take the place of learning the Gemara Rashi Tosphot Maharsha Maharam from Lublin. ]