Neural networks most certainly go through a process to transform input into output (even to mimic the results of another process) but it's a very different one from human neutral networks. But I think this is the crucial point of the debate, essentially unchanged from Searle's "Chinese Room" argument from decades ago.

The person in that room, looking up a dictionary with Chinese phrases and patterns, certainly follows a process, but it's easy to dismiss the notion that the person understands Chinese. But the question is if you zoom out, is the room itself intelligent because it is following a process, even if it's just a bunch of pattern recognition?