The issue is that Blizzard worded it VERY poorly.
Previously, you needed a Beta Account, Beta Launcher, and Beta Install to play Beta, and a PTR Account, PTR Launcher, and PTR Install to play PTR.
Now the "Beta Launcher and Install" are the same as PTR. And you have a normal, PTR, and Beta account.
I cannot play PTR on my Beta Account, and vice versa, as the GM (poorly) said, just as I cannot play Cata content on my older (and inactive) Wrath account.