The Catholic church clearly uses the scientific method when it comes to natural events.
And you miss the point. The church STARTS by asserting that a whole host of events, both historical and on-going, are not natural events. Those events are ignored in terms of the scientific method.
And they often only pay lip service to claims of scientific evaluation. It doesn't take much digging around in the miracle claims for beatification, things like eucharistic miracles and the ever present Marian visitations(just for a few random examples) to see that a lot of "evidence" is just hand-waving over dubious claims.
You use the scientific method when you want to prove or disprove natural events or processes. I don't see why you'd use it to determine if X belief is heretical to Catholicism.
Hmm, all of those papal encyclicals, catechisms and other teachings are obviously out of date, then, since they often make claims about physical processes which are very much in the area of scientific investigation. You should mention this to your bishop, so he can pass it on.
They use it when studying the stars, biology, etc.
Ah, that's why they have jettisoned the idea of a single couple as the genesis of the whole human race as it's scientifically untenable. Oh, wait, they didn't. That's defined in Humani Generis:
When, however, there is question of another conjectural opinion, namely polygenism, the children of the Church by no means enjoy such liberty. For the faithful cannot embrace that opinion which maintains that either after Adam there existed on this earth true men who did not take their origin through natural generation from him as from the first parent of all, or that Adam represents a certain number of first parents.
So, no, a basic fact of human evolution is ignored because of its theological implications. That's not a scientific viewpoint.
Granted they may not be AS thorough and not seek to find a natural explanation for one of those events once they've exhausted what modern science can tell us.
They don't even go that far. Hell, they've even regressed in modern times, since JPII gutted the office of the Promotor fide(better known as the Devil's Advocate). It wasn't rigorous before; now it's a rubber stamp. And don't get me started on exorcisms.
I was a Catholic and active in apologetics for many years. This nonsense was a large part of what made believing in that church an untenable position.