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Dan got the Bell cell phone, Brian got the Sprint cell phone, and Joelle got the AT&T cell phone.
We know Dan didn't get the AT&T, so he could have gotten the Sprint or the Bell.

But someone else got the Sprint, so Dan had to get the Bell.
Furthermore, we know that it was Brian who got the Sprint, because he is the only man in the group besides Dan.
So that leaves Joelle with the AT&T.

Frances says

The conclusion is correct, but the logic is completely wrong.
When Dan says he didn't order from AT&T then we know that he didn't.
When Brian says that he thought Dan ordered from AT&T then we know that Brian didn't order from AT&T either (assuming he knows that there was only one AT&T order).
Therefore Joelle ordered the AT&T phone.
We know that Brian ordered from Sprint because he's described as "the guy who ordered from Sprint", and therefore Dan ordered from Bell.

However... when the puzzle says, "That was all the man at the counter needed to know", this is wrong.
Unless Brian is wearing a sign that says, "the guy who ordered from Sprint", or maybe a baseball cap with a Sprint logo, the man at the counter has absolutely no way to know whether Dan or Brian ordered a Sprint phone.

The puzzle is broken as is, but could be fixed by changing the line that says:
The guy who ordered from Sprint says: "Oh, I thought you did".to
The guy wearing an "I hate Bell" t-shirt says: "Oh, I thought you did".

In the modified puzzle, we can see that Brian didn't order from AT&T (unless he doesn't know only one AT&T phone was ordered), and that he would never order from Bell.