It is improbable to the point of impossibility, and somewhat worse than you've outlined.

To stop just me a device/service that prevented dling a stream would need:

-strong end-to-end encryption, otherwise you'd just grab the packets to recreate the stream, then save it.

-to be self contained, otherwise you'd just grab the stream from the audio/video output.

-to be tamper-proof, otherwise you'd just bypass the software by messing with the hardware.