Well the app on iOS certainly can't "spy" on you in any meaningful way.

It can't tell what music or podcasts you are listening to, Apple doesn't give apps access like that.

I guess in theory the headphones could spy on you. They could run audio fingerprinting code, like Shazam, to identify what you are listening to.

The app could then feed that data back to Bose (or wherever).

But that sounds very unlikely, I'm calling bullshit on this spying claim until someone provides some actual evidence of it happening