MVP, you are actually very wrong. The Beta Classic client is there for pretty much everyone. BLizzard already said they are leaving it there so people can uninstall the beta client. You can know if you have real beta by whether or not the beta client’s play button is grayed out or active.
If anyone has any further questions about any of this, I have a data thread posted with tldr and link to BLizzard’s blue post with what we know currently. Hope it helps.