The purifying of morality which develops through right effort and the noble eightfold path is not the prescribed morality of the precepts (training rules). The full passage from which your quote is taken (introduction to MN 118), shows a list of the levels of training beginning with mindfulness of breathing and progressing two steps above to the noble eightfold path, then further on to stream-entry and above. A stream- enterer does not achieve elimination of doubt by the mere following of rules, they need to prove for themselves that craving produces suffering, and renunciation results in the removal of suffering. This was achieved by the Buddha-to-be on his way to awakening, through employing right effort, and involves direct experience of both the harmful and beneficial effects:
"And as I remained thus heedful, ardent, & resolute, thinking imbued with sensuality arose in me. I discerned that 'Thinking imbued with sensuality has arisen in me; and that leads to my own affliction or to the affliction of others or to the affliction of both. It obstructs discernment, promotes vexation, & does not lead to Unbinding.”
"As I noticed that it leads to my own affliction, it subsided. As I noticed that it leads to the affliction of others… to the affliction of both… it obstructs discernment, promotes vexation, & does not lead to Unbinding, it subsided. Whenever thinking imbued with sensuality had arisen, I simply abandoned it, dispelled it, wiped it out of existence.”
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"And as I remained thus heedful, ardent, & resolute, thinking imbued with renunciation arose in me. I discerned that 'Thinking imbued with renunciation has arisen in me; and that leads neither to my own affliction, nor to the affliction of others, nor to the affliction of both. It fosters discernment, promotes lack of vexation, & leads to Unbinding.”—-MN 19
There are two forms of right speech, here is the mundane right speech the Buddha refers to when describing what the community of monks is “established” on, as contrasted with “developed”:
“And what is the right speech with effluents, siding with merit, resulting in acquisitions? Abstaining from lying, from divisive tale-bearing, from abusive speech, & from idle chatter. This is the right speech with effluents, siding with merit, resulting in acquisitions.”—MN 117