Stoicism is not about masking pain, but understanding that no one has control of their environment. To violently react to that which we cannot control is damaging to the individual.
A Stoic will grieve like anyone else, but find comfort in reason.
It seems to me that this article intentionally ignores a very central point: These men aren't practicing Stoicism. She seems to demonstrate pretty well that Stoicism might have great benefits for a lot of them, but the actual examples of "Stoicism" she shows are kind of the philosophical equivalent of Greenspunning. It has some features of Stoicism, but doesn't really embrace the whole.