In your hypothetical discussion, person B's response may or may not be too facile, but person A's argument is irredemably flawed. In addition to (knowingly or not) conflating multiple connotations of the word theory, he is also conflating multiple deotations of the word evolution. Evolution, meaning the gradual change of existing species into new species over time is, in even person A's logic, a fact. There are multiple ways of demonstrating this fact: molecular genetics, fossils, comparative anatomy and physiology, embryology and developmental biology, etc. Evolution can also refer to the theory of evolution by natural selection, which is a scientific theory that attempts to explain the mechanism behind the fact of evolutionary change in species.
In this light, perhaps the only proper response to person A is to tell him that his terms are poorly defined.