Granted, religion can give you a sense of peace when grieving, but, like I had previously stated, in my opinion it's grounded in a false sense of security.
Also, one point where that article completely misses the mark is that everything in religion doesn't need to be substituted with science. No, science cannot help a grieving mother, but that doesn't mean that she will never be able to deal with the death of a child without religion. Though more difficult, it's not impossible, like the article assumes.
With the help of family and friends it's very much possible. There are also secular support groups available for that kind of thing. And, for some, the idea that a loved one has ceased to exist after death may be easier to handle than the possibility that they may be suffering for all eternity in an afterlife.
So that article doesn't give an example of something that cannot be achieved without religion, merely something that can't be replaced by science.