Can destiny err, according to the Hadith: "And know that what befell you was not going to miss you, and what missed you was not going to befall you"?

The hadith does not contain anything to support the aforementioned understanding. The hadith encourages entrusting all matters to Allah, clarifying that He is the Doer of whatever He wills, and that what He has decreed does not exceed its bounds, in confirmation of His saying, the Almighty: "No disaster strikes upon the earth or among yourselves except that it is in a register before We create it." The meaning of this is that what befell you was not destined to miss you, and what missed you was not destined to befall you. It also encourages reliance on Allah (tawakkul), contentment (rida), and patience (sabr).