No.
Next simply finances the phone over the number of payments you choose. You make all the payments, you own the phone. For that matter, you can pay off the balance at any time, and you own the phone.
If you terminate a 2-year contract early, you get to keep the phone, but you have to pay the ETF penalty -- effectively paying off the implicit loan you got when you bought the phone.
There's a lot of misinformation flying around on this thread. You have to do the math to figure out whether Next works for you. There are a number of factors, but the easiest way to compare is to calculate the total cost of the phone (however you buy it) and the monthly service over 24 months. Assuming you keep the phone at the end of the 24 months removes that variable.
With AT&T's current rates, you'll pay less with either Next or an outright purchase, if your dataplan is 10GB/month or higher. The difference is $150 per phone on the plan. However, if your dataplan is 6GB/month or lower, a 2-year contract is cheaper, by $90 per phone.
An example: with 1 phone and 6GB/month, you pay $3,079 under a 2-year contract, and $3,169 under no contract or Next. But with 1 phone and 10GB/month, you pay $3,559 under a 2-year contract, and $3,409 under no contract or Next.