Clearly it's false that every and any atheist will cry out to God or starting believing in God during times of crisis. Even if the claim were true, however, there would be serious problems with it — serious enough that theists should find it troubling.
First, how can such experiences can generate authentic faith? Would God even want people to believe merely because they were under great pressure and very afraid? Can such a faith lead to a life of faith and love which is supposed to be the foundation of religions like Christianity?
This problem is made clear in what might be the earliest expression of this myth, although it doesn't use the same words. Adolf Hitler told Cardinal Michael von Faulhaber of Bavaria in 1936:
Man cannot exist without belief in God. The soldier who for three and four days lies under intense bombardment needs a religious prop.
A "faith" and a belief in God which exists merely as a reaction to the fear and danger in situations like war isn't a genuine religious faith, it's just a "religious prop." Some atheists have likened religious faith to a crutch, and if that analogy is ever true it's probably most true here. Theists should not try to promote their religion as a crutch, though.