(Equally-frustrated) In the Watch ESPN ATV app, navigate to the Settings menu, and you should see that you're signed in as AT&T U-Verse (or something similar - I see Comcast XFINITY on my ATV). If not, you're not doing something correctly.
The sign-in for the Watch ESPN ATV app for my sis and I was to navigate to our cable portal and sign in. While you're signed in to your cable account, launch the ATV app, navigate to the Settings menu and choose the "Verify your TV Provider" option, then choose the first option (AT&T U-verse). While you're signed into your U-Verse account and in the same browser, navigate to that URL on the ATV screen and follow those instructions - you may need to wait a few minutes before being informed of the activation.!
And, don't fret too much just yet. I'm on Comcast - which isn't approved for the Longhorn Network, but it's showing up on my ATV. And, when the SEC and Longhorn Networks were added - I didn't see them for a few days, and only after I signed out and back in again. Cheers. And, Hook'em Horns!