Unfortunately, the various private, non ex cathedra comments of Pope John Paul II on Origins have tended to be imprecise. What exactly did he mean by "a correctly understood teaching of Evolution"? The word "Evolution" means all sorts of things to all sorts of people, and a precise definition of terms is therefore desirable. Clearly, Darwin's general theory of Evolution has failed under searching scrutiny, and Natural Evolution is in the midst of a deep crisis of credibility.
The objective truth is that rigorous scientific disciplines - such as molecular biology, biochemistry and genetics - have revealed mindboggling complexity within very tiny cells, and the reality of irreducible complexity within even such tiny cells clearly speaks only of Design. Numerous scientists have also shown that life forms are only capable of passing on the existing genetic information already possessed by them, and thus Natural Evolution cannot occur.
Modern research, therefore, suggests strongly that Natural Evolution cannot be historically true and that God chose to institute only variety within kind. This is not Evolution; since truly new "higher" genetic information is not being transmitted, life forms can only change within definite limits or boundaries. Nor can Theistic Evolution truly be defined as Evolution (as argued in Chapter 12); when fully considered, it reduces down only to innumerable instances of divine intervention - in contradiction to the observable facts of all reality, namely, that God works on all created things through secondary causes.
Instead of generalized private statements, one looks for precise terminology from the Pope, affecting vital related foundational Origins and Original Sin doctrine, which is not yet fully clarified. Addressing the Academy at the Rome conference on "Origins and Evolution of Life" (October 22, 1996), Pope John Paul II rightly pointed out that "truth cannot contradict truth." He also stated that, "the exegete and the theologian must keep informed about the results achieved by the natural sciences."