The headphones work without the app, but the app is required for updates (the headphones have onboard software) and also if you want to manage the multipoint connection capability from your phone (which can be more convenient than doing it from the headphones and each device you want to connect to, but is not necessary to use the feature.)
I do not install vendor apps for BT peripherals, and have been through the QC and 700 series of headphones without using their app. Same for Google and Samsung BT earbuds.
Can you install an app and get updates for bugs or changes to equalizer, noise cancellation, or other features (wanted or unwantes)? Yes, but it is not required nor "required", whatever that means.
Is it FUD? It's fear, for sure. Uncertainly maybe. Doubt, not really.
An app that doesn't do that today is an app that could do that after an update tomorrow.
As for firmware... well the fact that something that just processes audio needs a firmware update demonstrates that the company isn't doing proper engineering. Proper engineering processes would be able to resolve just about anything with firmware before it gets released. Yes there "might" be bugs. No, those bugs shouldn't be severe. And regardless of proper engineering, a firmware that doesn't send telemetry back today is a firmware that could send telemetry after an update tomorrow.
So it is FUD? No. It's awareness of what's possible.
Apps get updated all the time, and most of the time the update is fine. That's not untrue. It doesn't change the fact that an app could be updated with new/additional telemetry. That's not untrue, either. Telemetry is nothing less than a data grab of my private information. What do I use, what do I do, where do I do it, blah blah. That's my data and no "business" has a right to it. That's also not untrue no matter what you think.
Headphones, wireless or not, should not "need" firmware updates. That's not untrue. If the device is not fit for use, then make a recall.
Bose has nice products. I've used several generations of QuietComfort headphones. But the fact remains that they offer an app for updates when it shouldn't be needed at all, and they strongly "request" that it's needed.
Wait until third parties "require" an app to be installed, and the headphones send audio as data to the app instead of calling itself a microphone, and the app then sends that data to wherever you don't want it to.
Bose, for example, "requires" an app to be installed. For "updates", they tell you. Updates... to headphones...?!