The actual event of Kisa is agreed upon by all Muslims, as it is narrated through Sunni chains as well. The wording of the hadith that we recite now may be questioned (not saying it's weak), however since the context is agreed upon we read it and there is no problem with it.

Many duas have not so strong narration. Many of the sermons of Imam Ali. However our scholars say that we are certain these are from the Infallible Imams for various reasons and therefore they are accepted.