All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The narration which you mentioned in the question is also reported by Ad-Daaraqutni . It is an authentic narration, and is classified as such by Al-Albaani
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The narration is not only evidence on the importance of sighting the moon, but it is evidence that sighting is a condition for confirming the beginning of the month of Ramadan. Therefore, the Muslims should seek to sight the moon of Ramadan on the night of the 29th of Sha’baan each year. If they see the moon, they should fast otherwise they should complete Sha'baan thirty days. For more benefit, please refer to Fatwa 90491.
As regards breaking one's pledge then this is an act of disobedience and not an act of disbelief unless one believes that this is permissible, as in this case he is denying what Allaah Says, and what the Prophet said, and this is disbelief without any doubt.
For more benefit, please refer to Fatwa 89470.
Allaah Knows best.