If the app was free, he's probably SOL.
No, because then you still have the issue of false advertising. For the full functionality you need the app. The app comes with conditions not presented at the time of purchase of the headphones, yet the capability is advertised, ergo a misleading sale.
There's lots of leverage here for an intelligent lawyer, and I suspect BOSE will soon make use of that staggering loophole under US law to cough up without admitting fault.