Connection: very important.
Frame: don't have. If you have a "frame," you're doing it wrong.
Be aware of your own biases and limitations when evaluating others. The frame in AT is exceptionally loose compared to other dances. I'd wager to say that it would be easy to consider it nonexistant or "noodle-armed" if one is speaking from a ballroom background. That doesn't mean connection can't exist anyhow. (I've followed basic things perfectly well with absolutely no physical connection at all.)
Just because it doesn't fit what you know to be "true" about partner dancing, or dancing in general, doesn't mean the teacher doesn't know what they're talking about.
...then again, there are plenty of teachers out there who don't know what they're talking about. And plenty of (ballroom) teachers out there who will teach with a frame...even if that shows they don't know what they're talking about.