This is the fundamental point that gets made and debated, again and again. I just don't agree that the stress is the same. Speaking as a person who is very prone to interview nerves, nothing evokes quite the same reaction in me, so it's not a valid predictor. Despite my terrible nerves in interviews, I'm able to handle real-world stress just fine. In fact, the craziest example of this I have is live-coding demands from a client in response to a final deliverable. I had our codebase up in an editor on my laptop, and in response to client complaints, was making changes live and deploying to our UAT environment to prompt them to give the final sign-off. Literally, the difference between "ok, we will call this project complete and pay you for the last 6 months of your work" and "this is unacceptable, we aren't paying for this" was in my hands, over the span of an hour, with the client sitting right across from me.
This completely contradicts the argument that a candidate who has difficulty handling interview stress will not have the ability to handle any stress. I can't speak for everyone who gets nervous during interviews, but in my case it's due to the combination of the uncomfortable environment, lack of access to tools I've grown to rely on, and an awareness of how fickle people's opinions are.