A little over dramatic I think. In both cases, they were not aware of a tire failure because other aircraft reported debris on the runway. They had no indications of any damage and were flying over land the entire flight. If the situation got worse, they could have diverted at any moment. Instead, they continued to decrease their landing weight while continuing to the destination.

Continuing to the destination is the best/equally best decision to make for most (in terms of actual occurrences in day-to-day operations) abnormal situations.