“Before that, the miracles were thought to be just that, miracles.”
That is not true. Modern science didn’t invent the idea of Nature and natural laws that governed everything. The idea of every (public) miracle having an “out” is a Ramban in Chumash by the splitting of the Yam Suf.
But I don’t think the “out” argument is being used by DaMoshe properly. It’s not that natural means are an illusion. Rather Ramban says that when Hashem does nissim, they are done by as natural means as possible. So the splitting of the sea was done with a very strong wind. Under normal circumstances a even a very strong wind would not accomplish the full fledged splitting of the sea, but the use of the wind allows a person to say “maybe it was just a freak wind, very strong but very local.”
To carry that argument over to evolution one would have to say that the reason Hashem used evolution as the means of bringing about the incredible Human Being, is so that a person could say “maybe the intelligent Human with his capacity for moral choice and his incredible brain power and creativity was just a fluke of evolution, a happy accident.”