>I mean it's pretty easy to prove that's not true. Just stick it on a network and check the network traffic.

It's pretty easy to hide that network traffic too. Just save/compress everything to the local device and pipe it over when the phone/app is being used. (ever wonder why those apps take up so much memory and use up so much battery?).

Is there a simple app that notifies users about changes in internet traffic patterns of IoT devices on their networks?

You can't trust the devices themselves to tell you that, so the best approach is to put them behind a (hardware) firewall that protects both ways, not just from external connections but also to prevent devices to call home if their behavior is unclear.

Yes UniFi by Ubiquiti. There’s a price for admission.